EXISTENCE RESULT FOR NONUNIFORMLY DEGENERATE SEMILINEAR ELLIPTIC SYSTEMS IN^N

Abstract

Abstract. We study the existence of solutions for a class of nonuniformly degenerate elliptic systems in ‫ޒ‬ N , N ≥ 3, of the form

On a Neumann Problem at Resonance for Nonuniformly Semilinear Elliptic Systems in an Unbounded Domain With Nonlinear Boundary Condition

“…With similar arguments as those used in the proof of Lemma 2.3 in [4], we infer that the functional J i0 : E i → R (i = 1, 2) given by…”

ON EXISTENCE OF WEAK SOLUTIONS OF NEUMANN PROBLEM FOR QUASILINEAR ELLIPTIC EQUATIONS INVOLVING p-LAPLACIAN IN AN UNBOUNDED DOMAIN

“…We just remember the papers [1,2,4,3], [10,12,13,16], where different techniques of finding solutions are illustrated. We also find that in the case that h(x) ∈ L 1 loc (Ω), the quasilinear elliptic equations of type (1.1), with Dirichlet boundary condition, have been studied by D. M. Duc, N. T. Vu ( [7]), H. Q. Toan, N. Q. Anh, N. T. Chung (see [15,14,5]). The goal of this work we study the existence of weak solutions of Neumann problem for quasilinear elliptic equations with singular coefficients involving the p-Laplace operator of type (1.1) in an unbounded domain Ω ⊂ R N with sufficiently smooth bounded boundary ∂Ω.…”

Existence of Weak Non-Negative Solutions for a Class of Nonuniformly Boundary Value Problem

“…where [9,21,22]). We point out that the condition (1.2) implies that f has to be superlinear at infinity.…”