EXISTENCE OF SOLUTIONS FOR ASYMPTOTICALLY ‘LINEAR’ ${p}$-LAPLACIAN EQUATIONS

Abstract

Under very general conditions, a proof is given, via Morse theory, of the existence of solutions for asymptotically ‘linear’ p-Laplacian equations, where the asymptotic limit may be greater than the second eigenvalue. The existence of nonzero solutions is also considered. 2000 Mathematics Subject Classification 35J65, 58E05.