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Saddle type solutions for a class of reversible elliptic equations. (English) Zbl 1335.35064

Authors’ abstract: This paper is concerned with the existence of saddle type solutions for a class of semilinear elliptic equations of the type \[ \Delta u(x)+F_u(x,u), \quad x\in \mathbb{R}^n, \quad n\geq 2, \]
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.

MSC:

35J61 Semilinear elliptic equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35J20 Variational methods for second-order elliptic equations
34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
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Full Text: Euclid