Existence of weak solutions for a class of nonuniformly nonlinear elliptic equations in unbounded domains

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.…”

On the Existence of Weak Solutions for a Degenerate and Singular Elliptic System in ℝ N

“…This interesting idea came from the Mountain pass theorem for weakly continuously differentiable functionals introduced by D.M. Duc (see [9,14] and [17]). In the above papers, the coercivity of the functions a(x) and b(x) play an important role in the authors' arguments, i.e.…”

“…Then, system (1.1) now may be a degenerate and singular semilinear elliptic system. We also do not require in this work the coercivity for the functions a(x) and b(x) as in [6,7,15,17] and [18]. Such problems come from the consideration of standing waves in anisotropic Schrödinger systems.…”

“…For more information and connection on problems of this type, the readers may consult in [13,16] and the references therein. Our paper is motivated by the recent results in [4,6,10,12] and [17]. In order to state our main result, we first introduce some hypotheses below.…”