# Mathematische Nachrichten

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

### 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 (singular case) and $p>2$. In the first one, the reaction $f\left(z,x\right)$ is linear grow near $±\infty$ and resonant with respect to a nonprincipal nonnegative eigenvalue. In the second case, the reaction $f\left(z,·\right)$ is ( $p-1$)‐superlinear near $±\infty$ 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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