Resonance Problems For Nonlinear Elliptic Equations With Nonlinear Boundary Conditions

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Journal Of Applied Functional Analysis


We study the solvability of nonlinear second order elliptic partial differential equations with nonlinear boundary conditions where we impose asymptotic conditions on both nonlinearities in the differential equation and on the boundary in such a way that resonance occurs at a generalized eigenvalue; which is an eigenvalue of the linear problem in which the spectral parameter is both in the differential equation and on the boundary. The proofs are based on some variational techniques and topological degree arguments.


nonlinear elliptic equations, nonlinear boundary conditions, weighted Robin-Neumann-Steklov eigenproblem, resonance conditions