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.


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
Full Text: Euclid