(p,2)-equations asymmetric at both zero and infinity

Abstract

We consider a (p,2){(p,2)}-equation, that is, a nonlinear nonhomogeneous elliptic equation driven by the sum of a p-Laplacian and a Laplacian with p>2{p>2}. The reaction term is (p-1){(p-1)}-linear, but exhibits asymmetric behavior at ±∞{\pm\infty} and at 0±{0^{\pm}}. Using variational tools, together with truncation and comparison techniques and Morse theory, we prove two multiplicity theorems, one of them providing sign information for all the solutions (positive, negative, nodal).

Keywords

• asymmetric reaction
• resonance
• fučik spectrum
• constant sign solutions
• nodal solution
• critical groups
• morse relation
• 35j20
• 35j60
• 58e05