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

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  • Tieshan He
  • Youfa Lei
  • Meng Zhang
  • Hongying Sun

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.

Suggested Citation

  • Tieshan He & Youfa Lei & Meng Zhang & Hongying Sun, 2018. "Nodal solutions for resonant and superlinear (p, 2)‐equations," Mathematische Nachrichten, Wiley Blackwell, vol. 291(17-18), pages 2565-2577, December.
    • Handle: RePEc:bla:mathna:v:291:y:2018:i:17-18:p:2565-2577
    DOI: 10.1002/mana.201700163
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