Infinitely many solutions for quasilinear elliptic equations involving double critical terms and boundary geometry

Abstract

Abstract. In this paper, we study the following problemC 2 bounded domain with 0 ∈Ω and a ∈ C 1 (Ω). By an approximation argument, we prove that if N > p 2 + p, a(0) > 0 and Ω satisfies some geometry conditions if 0 ∈ ∂Ω, for example, all the principle curvatures of ∂Ω at 0 are negative, then the above problem has infinitely many solutions.

Infinitely many solutions for an elliptic problem with double critical Hardy-Sobolev-Maz'ya terms

“…However, in this case, our condition is much weaker than their's. For the details, one can refer to [44].…”

On the eigengraph for p-biharmonic equations with Rellich potentials and weight

“…Nonlinear eigenvalue problems involving Rellich potential have been studied by many authors; see e.g. [2,4,6]. The study of eigencurve problems is a subject of several works, see [1,5] and the references therein.…”