{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T10:25:35Z","timestamp":1774952735406,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,2,15]],"date-time":"2019-02-15T00:00:00Z","timestamp":1550188800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we consider the second order discontinuous differential equation in the real line,       a  t , u   \u03d5   u \u2032    \u2032  = f  t , u ,  u \u2032   ,  a . e . t \u2208 R , u  ( \u2212 \u221e )  =  \u03bd \u2212  ,   u  ( + \u221e )  =  \u03bd +  ,     with    \u03d5    an increasing homeomorphism such that     \u03d5 ( 0 ) = 0     and     \u03d5 ( R ) = R    ,     a \u2208 C (  R 2  , R )     with     a ( t , x ) &gt; 0     for      ( t , x )  \u2208  R 2     ,     f :  R 3  \u2192 R     a     L 1    -Carath\u00e9odory function and      \u03bd \u2212  ,  \u03bd +  \u2208 R     such that      \u03bd \u2212  &lt;  \u03bd +     . The existence and localization of heteroclinic connections is obtained assuming a Nagumo-type condition on the real line and without asymptotic conditions on the nonlinearities    \u03d5    and     f    . To the best of our knowledge, this result is even new when     \u03d5 ( y ) = y    , that is for equation       a  t , u ( t )   u \u2032   ( t )   \u2032  = f  t , u  ( t )  ,  u \u2032   ( t )   ,  a . e . t \u2208 R    . Moreover, these results can be applied to classical and singular    \u03d5   -Laplacian equations and to the mean curvature operator.<\/jats:p>","DOI":"10.3390\/axioms8010022","type":"journal-article","created":{"date-parts":[[2019,2,17]],"date-time":"2019-02-17T22:11:50Z","timestamp":1550441510000},"page":"22","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Heteroclinic Solutions for Classical and Singular \u03d5-Laplacian Non-Autonomous Differential Equations"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7485-2500","authenticated-orcid":false,"given":"Feliz","family":"Minh\u00f3s","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Escola de Ci\u00eancias e Tecnologia, Centro de Investiga\u00e7\u00e3o em Matem\u00e1tica e Aplica\u00e7\u00f5es (CIMA), Instituto de Investiga\u00e7\u00e3o e Forma\u00e7\u00e3o Avan\u00e7ada, Universidade de \u00c9vora. Rua Rom\u00e3o Ramalho, 59, 7000-671 \u00c9vora, Portugal"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1186\/1687-2770-2011-26","article-title":"On the solvability of a boundary value problem on the real line","volume":"2011","author":"Cupini","year":"2011","journal-title":"Bound. Value Probl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1186\/1687-2770-2013-252","article-title":"The role of boundary data on the solvability of some equations involving non-autonomous nonlinear differential operators","volume":"2013","author":"Marcelli","year":"2013","journal-title":"Bound. 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