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

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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 < p < 2 (singular case) and p > 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.

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