Existence of Weak Solutions for a Nonuniformly Elliptic Nonlinear System In

Abstract

We study the nonuniformly elliptic, nonlinear system − div(h1(x)∇u) + a(x)u = f(x, u, v) in R , − div(h2(x)∇v) + b(x)v = g(x, u, v) in R . Under growth and regularity conditions on the nonlinearities f and g, we obtain weak solutions in a subspace of the Sobolev space H1(RN , R2) by applying a variant of the Mountain Pass Theorem. 

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