Positive solutions for phi-Laplace equations with discontinuous state-dependent forcing terms
Articles
Radu Precup
Babe¸s-Bolyai University
Jorge Rodríguez-López
Universidade de Santiago de Compostela
Published 2019-04-23
https://doi.org/10.15388/NA.2019.3.8
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Keywords

discontinuous differential equation
φ-Laplacian problem
positive solution
fixed point
multivalued map
infinitely many solutions

How to Cite

Precup, R. and Rodríguez-López, J. (2019) “Positive solutions for phi-Laplace equations with discontinuous state-dependent forcing terms”, Nonlinear Analysis: Modelling and Control, 24(3), pp. 447–461. doi:10.15388/NA.2019.3.8.

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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