Pfluger, Klaus2019-03-252019-03-251998-04-10Pfluger, K. (1998). Existence and multiplicity of solutions to a p-Laplacian equation with nonlinear boundary condition. <i>Electronic Journal of Differential Equations, 1998</i>(10), pp. 1-13.1072-6691https://hdl.handle.net/10877/7946We study the nonlinear elliptic boundary value problem Au = ƒ(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 ℝN with non-compact boundary, and ƒ 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 ƒ, g is sublinear and the other one is superlinear. The proofs are based on variational methods applied to weighted function spaces.Text13 pages1 file (.pdf)enAttribution 4.0 Internationalp-LaplacianNonlinear boundary conditionVariational methodsUnbounded domainWeighted function spaceArticle