Multiple solutions for p-Laplacian type problems with asymptotically p-linear terms via a cohomological index theory

2013/10/02 by Anna María Candela, A. M. Candela, G. Palmieri +5
Computer Science · Mathematics · #35J35 #35J60 #35J92 #47J30 #58E05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #math.AP #msc:35J35 #msc:35J60 #msc:35J92 #msc:47J30 #msc:58E05

paper · pdf · doi:10.48550/arxiv.1310.0679

arxiv created 2013/10/02 · openalex publication_date 2013/10/02 · arxiv updated 2013/10/03 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is investigating the existence of weak solutions of the quasilinear elliptic model problem \- \divg (A(x,u) |∇ u|^p-2 ∇ u) + \dfrac1p A_t(x,u) |∇ u|^p = f(x,u) · \hboxin Ω,
u = 0 · \hboxon ∂Ω, . where Ω⊂ \R^N is a bounded domain, N≥ 2, p > 1, A is a given function which admits partial derivative A_t(x,t) = (∂ A)/(∂ t)(x,t) and f is asymptotically p-linear at infinity. Under suitable hypotheses both at the origin and at infinity, and if A(x,⋅) is even while f(x,⋅) is odd, by using variational tools, a cohomological index theory and a related pseudo--index argument, we prove a multiplicity result if p > N in the non--resonant case.

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