Existence and Multiplicity of Solutions to a p-Laplacian Equation with Nonlinear Boundary Condition
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We study the nonlinear elliptic boundary value problem Au = f(x,u) in Ω, Bu = g(x,u) on ∂Ω, where A is an operator of p-Laplacian type, Ω is an unbounded domain in ℝ(N) with non-compact boundary, and f and g are subcritical nonlinearities. We show existence of a nontrivial nonnegative weak solution when both f and g are superlinear. Also we show existence of at least two nonnegative solutions when one of the two functions f, g is sublinear and the other one is superlinear. The proofs are based on variational methods applied to weighted function spaces.