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Multiple solutions for Neumann and periodic problems with singular \(\phi \)-Laplacian. (English) Zbl 1241.35076
This paper is concerned with the existence of multiple solutions for semilinear elliptic equations that may be written as power-type perturbations of the mean curvature operator. The equations are complemented with homogeneous Neumann boundary conditions or periodic conditions in the 1-dimensional case. By means of variational methods which combine critical point theory in the spirit of Szulkin with Ekeland’s variational principle and the mountain pass theorem, the authors obtain nice multiplicity results of radial solutions for small values of parameters.

MSC:
35J61 Semilinear elliptic equations
35J66 Nonlinear boundary value problems for nonlinear elliptic equations
35J20 Variational methods for second-order elliptic equations
35A15 Variational methods applied to PDEs
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