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      Positive solutions for φ-Laplace equations with discontinuous state-dependent forcing terms

      1 , 2

      Nonlinear Analysis: Modelling and Control

      Vilnius University Press

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          Abstract

          This paper concerns the existence, localization and multiplicity of positive solutions for a φ-Laplacian problem with a perturbed term that may have discontinuities in the state variable. First, the initial discontinuous differential equation is replaced by a differential inclusion with an upper semicontinuous term. Next, the existence and localization of a positive solution of the inclusion is obtained via a compression-expansion fixed point theorem for a composition of two multivalued maps, and finally, a suitable control of discontinuities allows to prove that any solution of the inclusion is a solution in the sense of Carathéodory of the initial discontinuous equation. No monotonicity assumptions on the nonlinearity are required.

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          Most cited references 27

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          Differential Equations with Discontinuous Righthand Sides

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            Patchy Vector Fields and Asymptotic Stabilization

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              Discontinuous differential equations, I

               Otomar Hájek (1979)
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                Author and article information

                Journal
                Nonlinear Analysis: Modelling and Control
                Vilnius University Press
                1392-5113
                April 23 2019
                April 23 2019
                : 24
                : 3
                : 447-461
                Affiliations
                [1 ]Department of Mathematics, Babes-Bolyai University, Romania
                [2 ]Instituto de Matemáticas, Universidade de Santiago de Compostela, Spain
                Article
                10.15388/NA.2019.3.8
                © 2019

                All content is freely available without charge to users or their institutions. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission of the publisher or the author. Articles published in the journal are distributed under a http://creativecommons.org/licenses/by/4.0/.

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                Self URI (journal page): http://www.journals.vu.lt/

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