Existence and multiplicity of solutions to a p-Laplacian equation with nonlinear boundary condition
نویسنده
چکیده
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 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 superlinear. The proofs are based on variational methods applied to weighted function spaces.
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