The goal of this paper is to study the existence of non-trivial weak solutions for the nonuniformly nonlinear elliptic equation - div (h (x) ∇ u) + q (x) u = f (x, u) in an unbounded domain Ω ⊂ R^N (N ≥ 3), where h (x) ∈ L_loc¹ (Ω). The solutions will be obtained in a subspace of the Sobolev space H₀¹ (Ω) and the proofs rely essentially on a variation of the Mountain pass theorem in [D.M. Duc, Nonlinear singular elliptic equations, J. London. Math. Soc. 40 (2) (1989) 420-440]. © 2008 Elsevier Ltd. All rights reserved.

Toan H.Q., Chung N.T.

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Từ khóa : Landforms; Navier Stokes equations; Existence of weak solutions; Mountain pass theorem; Non-linear elliptic equations; Non-trivial; Nonuniformly elliptic equations; Singular elliptic equations; Sobolev spaces; The weakly continuously differentiable functional; Unbounded domains; Weak solutions; Nonlinear equations