An Asymmetric Steklov Problem With Weights: the singular case

Abstract

abstract:We prove the existence of a first nonprincipal eigenvalue for an asymmetric Steklov problem with weights. We are interested in the singular case (in where one of the weights has meanvalue zero), this case requires some special attention in connection with the Palais Smale (P S) conditions and with the mountain pass geometry.

On Steklov–Neumann boundary value problems for some quasilinear elliptic equations

“…In [9][10][11], the authors considered the nonlinear Neumann problem where p = 2, while the same problem involving the p-Laplacian was studied by [12][13][14][15]. Some previous studies have treated the nonlinear Steklov problem, but only [16,17] considered p = 2 and [18] dealt with p > 1.…”

ON STEKLOV BOUNDARY VALUE PROBLEMS FOR p(x)-LAPLACIAN EQUATIONS Vol. 5(2) July 2017, No. 28, pp. 289-297 I. EKINCIOGLU, R. AYAZOGLU(MASHIYEV)

“…in H 1 ( ) with respect to the speci…c inner products. Some previous studies have treated the nonlinear Steklov problem, but only [4] considered p = 2 and [21] dealt with p > 1. The inhomogeneous Steklov problems involving the p-Laplacian has been the object of study in, for example, [19] , in which the authors have studied this class of inhomogeneous Steklov problems in the cases of p(x) p = 2 and of p(x) p > 1, respectively.…”