A priori bounds and multiplicity results for slightly superlinear and sublinear elliptic p-Laplacian equations

2022/11/28 by Chaouai, Zakariya, Tamaazousti, Mohamed
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2211.15222

Abstract

We consider the following problem -Δ_pu= h(x,u) in Ω, u∈ W^1,p₀(Ω), where Ω is a bounded domain in ℝ^N, 1(N)/(p) and they are without sign condition. Firstly, we show a priori bound on solutions, then by using variational arguments, we prove the existence of at least two nonnegative solutions. One of the main difficulties is that the nonlinearity term h(x,u) does not satisfy the standard Ambrosetti and Rabinowitz condition.

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