NEW MULTIPLE SOLUTIONS FOR SOME PERIODIC BOUNDARY VALUE PROBLEMS WITH ψ-LAPLACIAN

Abstract

We study the existence of multiple solutions of the quasilinear equation
(ψ(u'(t)))'= f(t,u(t),u'(t)), t∈[0,T]
submitted to periodic boundary conditions, where ψ:]-a,a[→R, with 0<a < +∞, is an increasing homeomorphism such that ψ(0)=0. Combining some sign conditions and lower and upper solutions method, we obtain existence of two or Three solutions.