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On nonlinear elliptic problems with discontinuities. (English) Zbl 1072.35072

The authors utilize degree theoretic methods in order to examine a quasilinear resonant problem driven by the \(p\)–Laplacian and with a discontinuous forcing term and prove three existence theorems. The first theorem is a multiplicity result. Using the method of upper and lower solutions, the authors demonstrate the existence of the bounded solutions, one strictly positive and the other strictly negative. The other two theorems concern a resonant eigenvalue problem and establish the existence of a solution using Landesman-Lazer type conditions.

MSC:

35J60 Nonlinear elliptic equations
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