Infinitely many arbitrarily small positive solutions for the Dirichlet problem involving the p-Laplacian
- 1 June 2002
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Vol. 132 (3) , 511-519
- https://doi.org/10.1017/s030821050000175x
Abstract
In this paper we present a result of existence of infinitely many arbitrarily small positive solutions to the following Dirichlet problem involving the p-Laplacian, where Ω ∈ RN is a bounded open set with sufficiently smooth boundary ∂Ω, p > 1, λ > 0, and f: Ω × R → R is a Carathéodory function satisfying the following condition: there exists t̄ > 0 such that Precisely, our result ensures the existence of a sequence of a.e. positive weak solutions to the above problem, converging to zero in L∞(Ω).Keywords
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