Resonance for some nonlinear second order elliptic equations
Nsoki Mavinga
Abstract:
We are concerned with the solvability of linear second order elliptic partial differential equations with nonlinear boundary conditions by imposing asymptotic conditions
of nonuniform type with respect to the Steklov spectrum on the boundary nonlinearity. We cast the problem in terms of nonlinear compact perturbations of the identity
on appropriate trace spaces in order to prove the existence of strong solutions. We
obtain a priori estimates for possible solutions to a homotopy on suitable trace spaces
and use topological degree arguments.