Topological Methods in Nonlinear Analysis

Nodal solutions for nonlinear nonhomogeneous Neumann equations

Sergiu Aizicovici, Nikolaos S. Papageorgiou, and Vasile Staicu

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Abstract

We consider a nonlinear Neumann problem driven by a nonhomogeneous differential operator with a Caratheodory reaction which is $(p-1)$-sublinear near $\pm\infty$. Using variational tools we show that the problem has at least three nontrivial smooth solutions (one positive, one negative and a third nodal). Our formulation unifies problems driven by the $p$-Laplacian, the $(p,q)$ Laplacian and the $p$-generalized mean curvature operator.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 43, Number 2 (2014), 421-438.

Dates
First available in Project Euclid: 11 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1460381516

Mathematical Reviews number (MathSciNet)
MR3236978

Zentralblatt MATH identifier
1371.35130

Citation

Aizicovici, Sergiu; Papageorgiou, Nikolaos S.; Staicu, Vasile. Nodal solutions for nonlinear nonhomogeneous Neumann equations. Topol. Methods Nonlinear Anal. 43 (2014), no. 2, 421--438. https://projecteuclid.org/euclid.tmna/1460381516


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