Multiplicity results for some elliptic problems with nonlinear boundary conditions involving variable exponents
In this paper we analyze an elliptic partial differential equation involving variable exponent growth conditions coupled with a nonlinear boundary condition. We show the existence of infinitely many bounded weak solutions provided there is a suitable oscillatory behavior of the nonlinearity either at infinity or at zero. Our proofs rely on a method due to Saint Raymond.
variable exponent weak solution oscillatory behavior