Special Session 5: Recent results in Nonlinear PDEs

Nodal Solutions for nonlinear elliptic equations

Michael E Filippakis
University of Piraeus, Department of Digital Systems,
Greece
Co-Author(s):    Nikolaos S.Papageorgiou
Abstract:
We consider a nonlinear nonhomogeneous eliptic equation driven by the sum of a $p$-Laplacian and of $q$-Laplacian(a $(p,q)$-equation). The reaction term is a Caratheodory function which is resonant at $\pm\infty$ with respect to any nonprincipal variational eigenvalue of the Robin $p$-Laplacian. Morse theory (critical groups) with variational methods), help us to prove the existence of at least three nontrivial smooth solutions. \footnote{The publication of this paper has been partly supported by the University of Piraeus Research Center}}