Nodal solutions for resonant and superlinear (p, 2)‐equations

Tieshan He, Youfa Lei, Meng Zhang and Hongying Sun

Mathematische Nachrichten, 2018, vol. 291, issue 17-18, 2565-2577

Abstract: We consider nonlinear, nonhomogeneous elliptic Dirichlet equations driven by the sum of a p‐Laplacian and a Laplacian (so‐called (p, 2)‐equation). We are concerned with both cases 1 2. In the first one, the reaction f(z,x) is linear grow near ±∞ and resonant with respect to a nonprincipal nonnegative eigenvalue. In the second case, the reaction f(z,·) is (p−1)‐superlinear near ±∞ and has z‐dependent zeros of constant sign. Using variational methods together with flow invariance arguments, we establish the existence of nodal solutions.

Date: 2018
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