Multiplicity results for elliptic problems with super-critical concave and convex nonlinearties

2017/06/26 by Kuhestani, Najmeh, Moameni, Abbas
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1706.08385

Abstract

We shall prove a multiplicity result for semilinear elliptic problems with a super-critical nonlinearity of the form, \ -Δu =|u|^p-2 u+μ|u|^q-2u, · amp; x ∈ Ω
u=0, · amp; x ∈ ∂ Ω . where Ω⊂ ℝⁿ is a bounded domain with C²-boundary and 12, there exists μ^*>0 such that for each μ∈ (0, μ^*) this problem has a sequence of solutions with a negative energy. This result was already known for the subcritical values of p. In this paper, we shall extend it to the supercritical values of p as well. Our methodology is based on a new variational principle established by one of the authors that allows one to deal with problems beyond the usual locally compactness structure.

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