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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