Nodal solutions for (𝑝,2)-equations

Aizicovici, Sergiu; Papageorgiou, Nikolaos; Staicu, Vasile

doi:10.1090/S0002-9947-2014-06324-1

Nodal solutions for $\left (p,2\right )$-equations
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by Sergiu Aizicovici, Nikolaos S. Papageorgiou and Vasile Staicu PDF

Trans. Amer. Math. Soc. 367 (2015), 7343-7372 Request permission

Abstract:

In this paper, we study a nonlinear elliptic equation driven by the sum of a $p$-Laplacian and a Laplacian ($\left ( p,2\right )$-equation), with a Carathéodory $\left ( p-1\right )$-(sub-)linear reaction. Using variational methods combined with Morse theory, we prove two multiplicity theorems providing precise sign information for all the solutions (constant sign and nodal solutions). In the process, we prove two auxiliary results of independent interest.

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