(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).

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