NONLINEAR NEUMANN BOUNDARY VALUE PROBLEMS WITH φ−LAPLACIAN OPERATORS

Abstract

Using the Leray-Schauder degree theory we obtain existence results for Neumann boundary value problems (φ(u ′)) ′ = f(t, u, u ′), u ′ (0) = 0 = u ′ (T), where φ is an homeomorphism between R and]−a, a [ (or between]−a, a[ and R), φ(0) = 0 and f is a suitable nonlinearity. 1