{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:34:04Z","timestamp":1760060044994,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,3]],"date-time":"2025-08-03T00:00:00Z","timestamp":1754179200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Guizhou University Introduced Talent Research Project (2022)","award":["70","39"],"award-info":[{"award-number":["70","39"]}]},{"name":"Basic Research Project of Guizhou University (2023)","award":["70","39"],"award-info":[{"award-number":["70","39"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper focuses on exploring an impulsive stochastic differential variational inequality (ISDVI), which combines an impulsive stochastic differential equation and a stochastic variational inequality. Innovatively, our work incorporates two key aspects: first, our stochastic differential equation contains an impulsive term, enabling better handling of sudden event impacts; second, we utilize a non-local condition z(0)=\u03c70+\u03d1(z) that integrates measurements from multiple locations to construct superior models. Methodologically, we commence our analysis by using the projection method, which ensures the existence and uniqueness of the solution to ISDVI. Subsequently, we showcase the practical applicability of our theoretical findings by implementing them in the investigation of a stochastic consumption process and electrical circuit model.<\/jats:p>","DOI":"10.3390\/axioms14080603","type":"journal-article","created":{"date-parts":[[2025,8,5]],"date-time":"2025-08-05T08:46:55Z","timestamp":1754383615000},"page":"603","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Existence and Uniqueness of Solutions for Impulsive Stochastic Differential Variational Inequalities with Applications"],"prefix":"10.3390","volume":"14","author":[{"given":"Wei","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematical and Statistics, Guizhou University, Guiyang 550025, China"}]},{"given":"Kui","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematical and Statistics, Guizhou University, Guiyang 550025, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/0377-2217(93)90048-R","article-title":"A variational inequality formulation of the dynamic traffic assignment problem","volume":"71","year":"1993","journal-title":"Eur. J. Oper. Res."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Facchinei, F., and Pang, J.S. (2003). Finite-Dimensional Variational Inequalities and Complementarity Problems, Springer.","DOI":"10.1007\/b97544"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1007\/BF01448366","article-title":"A variational inequality approach to constrained control problems for parabolic equations","volume":"17","author":"Tiba","year":"1988","journal-title":"Appl. Math. Optim."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Aubin, J.P., and Cellina, A. (1984). Differential Inclusions: Set-Valued Maps and Viability Theory, Springer.","DOI":"10.1007\/978-3-642-69512-4"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1007\/s10107-006-0052-x","article-title":"Differential variational inequalities","volume":"113","author":"Pang","year":"2008","journal-title":"Math. Program."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1007\/s10107-013-0689-1","article-title":"Differential variational inequality approach to dynamic games with shared constraints","volume":"146","author":"Chen","year":"2014","journal-title":"Math. Program."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1007\/s10107-013-0669-5","article-title":"On a new class of differential variational inequalities and a stability result","volume":"139","author":"Gwinner","year":"2013","journal-title":"Math. Program."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/S0252-9602(16)30112-6","article-title":"Differential variational inequalities in infinite Banach spaces","volume":"37","author":"Liu","year":"2017","journal-title":"Acta Math. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1007\/s00033-018-0929-6","article-title":"A class of fractional differential hemivariational inequalities with application to contact problem","volume":"69","author":"Zeng","year":"2018","journal-title":"Z. Angew. Math. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"065006","DOI":"10.1088\/1361-6420\/ac61a5","article-title":"Inverse problems for generalized quasi-variational inequalities with application to elliptic mixed boundary value systems","volume":"38","author":"Cen","year":"2022","journal-title":"Inverse Probl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"6787","DOI":"10.1016\/j.jde.2016.01.012","article-title":"Evolutionary problems driven by variational inequalities","volume":"260","author":"Liu","year":"2016","journal-title":"J. Differ. Equ."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"969","DOI":"10.1080\/02331934.2022.2133544","article-title":"Coupled system of fractional hemivariational inequalities with applications","volume":"73","author":"Hao","year":"2024","journal-title":"Optimization"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"108098","DOI":"10.1016\/j.cnsns.2024.108098","article-title":"A new class of fractional Navier\u2013Stokes system coupled with multivalued boundary conditions","volume":"136","author":"Hao","year":"2024","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"104373","DOI":"10.1016\/j.nonrwa.2025.104373","article-title":"Existence and convergence analysis of second-order delay differential variational\u2013hemivariational inequalities with memory terms","volume":"85","author":"Hao","year":"2025","journal-title":"Nonlinear Anal. Real World Appl."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1007\/s00033-020-1260-6","article-title":"Evolutionary variational\u2013hemivariational inequalities with applications to dynamic viscoelastic contact mechanics","volume":"71","author":"Han","year":"2020","journal-title":"Z. Angew. Math. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"106718","DOI":"10.1016\/j.cnsns.2022.106718","article-title":"Applications of generalized fractional hemivariational inequalities in solid viscoelastic contact mechanics","volume":"115","author":"Han","year":"2022","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1007\/s12220-024-01545-5","article-title":"Regularity and Dirichlet problem for double-phase energy functionals of different power growth","volume":"34","author":"Vetro","year":"2024","journal-title":"J. Geom. Anal."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/s00245-024-10139-0","article-title":"On nonconvex perturbed fractional sweeping processes","volume":"89","author":"Zeng","year":"2024","journal-title":"Appl. Math. Optim."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"6183","DOI":"10.22436\/jnsa.009.12.23","article-title":"Mild solutions of impulsive semilinear neutral evolution equations in Banach spaces","volume":"9","author":"Hao","year":"2016","journal-title":"J. Nonlinear Sci. Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"6747","DOI":"10.1016\/j.na.2011.06.054","article-title":"Existence of global solutions for second order impulsive abstract partial differential equations","volume":"74","author":"Sivasankaran","year":"2011","journal-title":"Nonlinear Anal. Theory Methods Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1186\/s13660-022-02791-3","article-title":"An analysis concerning approximate controllability results for second-order Sobolev-type delay differential systems with impulses","volume":"2022","author":"Nisar","year":"2022","journal-title":"J. Inequalities Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"107560","DOI":"10.1016\/j.cnsns.2023.107560","article-title":"Approximate controllability analysis of impulsive neutral functional hemivariational inequalities","volume":"127","author":"Valliammal","year":"2023","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"5469","DOI":"10.1080\/00036811.2021.1895123","article-title":"(omega, c)-periodic solutions for time-varying non-instantaneous impulsive differential systems","volume":"101","author":"Liu","year":"2022","journal-title":"Appl. Anal."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2743","DOI":"10.1007\/s41980-021-00666-9","article-title":"A class of (omega, T)-periodic solutions for impulsive evolution equations of Sobolev type","volume":"48","author":"Liu","year":"2022","journal-title":"Bull. Iran. Math. Soc."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1489","DOI":"10.1515\/ms-2024-0108","article-title":"Periodic Solutions for Conformable Non-autonomous Non-instantaneous Impulsive Differential Equations","volume":"74","author":"Ding","year":"2024","journal-title":"Math. Slovaca"},{"key":"ref_26","first-page":"1","article-title":"Properties of the solutions to periodic conformable non-autonomous non-instantaneous impulsive differential equations","volume":"2024","author":"Ding","year":"2024","journal-title":"Electron. J. Differ. Equ."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/s10107-016-0995-5","article-title":"Stochastic variational inequalities: Single-stage to multistage","volume":"165","author":"Rockafellar","year":"2017","journal-title":"Math. Program."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2644","DOI":"10.1137\/22M1517111","article-title":"Asymptotically autonomous robustness in probability of random attractors for stochastic Navier-Stokes equations on unbounded Poincar\u00e9 domains","volume":"55","author":"Wang","year":"2023","journal-title":"SIAM J. Math. Anal."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Wang, R., and Chen, P. (2024). Enhanced Mean Random Attractors for Nonautonomous Mean Random Dynamical Systems in Product Bochner Spaces. Commun. Math. Stat., 1\u201330.","DOI":"10.1007\/s40304-024-00396-4"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Yang, M., Lv, T., and Wang, Q. (2023). The averaging principle for Hilfer fractional stochastic evolution equations with L\u00e9vy noise. Fractal Fract., 7.","DOI":"10.3390\/fractalfract7100701"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"386","DOI":"10.1016\/j.aej.2024.07.111","article-title":"Hilfer fractional stochastic evolution equations on the positive semi-axis","volume":"104","author":"Yang","year":"2024","journal-title":"Alex. Eng. J."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"107577","DOI":"10.1016\/j.cnsns.2023.107577","article-title":"Euler scheme for solving a class of stochastic differential variational inequalities with some applications. Commun","volume":"127","author":"Zhang","year":"2023","journal-title":"Nonlinear Sci. Numer. Simul."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"114372","DOI":"10.1016\/j.chaos.2023.114372","article-title":"A stochastic fractional differential variational inequality with L\u00e9vy jump and its application","volume":"178","author":"Zeng","year":"2024","journal-title":"Chaos Solitons Fractals"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"103889","DOI":"10.1016\/j.nonrwa.2023.103889","article-title":"Penalty method for solving a class of stochastic differential variational inequalities with an application","volume":"73","author":"Zhang","year":"2023","journal-title":"Nonlinear Anal. Real World Appl."},{"key":"ref_35","first-page":"199","article-title":"A new class of fractional impulsive differential hemivariational inequalities with an application","volume":"27","author":"Weng","year":"2022","journal-title":"Nonlinear Anal. Model. Control"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"3768","DOI":"10.1137\/080725258","article-title":"Convergence of time-stepping schemes for passive and extended linear complementarity systems","volume":"47","author":"Han","year":"2009","journal-title":"SIAM J. Numer. Anal."},{"key":"ref_37","unstructured":"Haase, H., Garbe, H., and Gerth, H. (2009). Grundlagen der Elektrotechnik, Sch\u00f6neworth."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"112023","DOI":"10.1016\/j.chaos.2022.112023","article-title":"A Monte-Carlo approach for pricing arithmetic Asian rainbow options under the mixed fractional Brownian motion","volume":"158","author":"Ahmadian","year":"2022","journal-title":"Chaos Solitons Fractals"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/8\/603\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:22:21Z","timestamp":1760034141000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/8\/603"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,3]]},"references-count":38,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2025,8]]}},"alternative-id":["axioms14080603"],"URL":"https:\/\/doi.org\/10.3390\/axioms14080603","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,8,3]]}}}