Advances in Differential Equations

Saddle type solutions for a class of reversible elliptic equations

Francesca Alessio, Giuseppina Alessio, and Piero Montecchiari

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This paper is concerned with the existence of saddle type solutions for a class of semilinear elliptic equations of the type \begin{equation} \Delta u(x)+F_{u}(x,u)=0,\quad x\in\mathbb R^{n},\;\; n\ge 2, \tag*{(PDE)} \end{equation} where $F$ is a periodic and symmetric nonlinearity. Under a non degeneracy condition on the set of minimal periodic solutions, saddle type solutions of $(PDE)$ are found by a renormalized variational procedure.

Article information

Adv. Differential Equations, Volume 21, Number 1/2 (2016), 1-30.

First available in Project Euclid: 23 November 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J60: Nonlinear elliptic equations 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 35B40: Asymptotic behavior of solutions 35J20: Variational methods for second-order elliptic equations 34C37: Homoclinic and heteroclinic solutions


Alessio, Francesca; Alessio, Giuseppina; Montecchiari, Piero. Saddle type solutions for a class of reversible elliptic equations. Adv. Differential Equations 21 (2016), no. 1/2, 1--30.

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