Electron. J. Diff. Equ., Vol. 2015 (2015), No. 103, pp. 1-18.

Positive solutions for parametric nonlinear periodic problems with competing nonlinearities

Sergiu Aizicovici, Nikolaos S. Papageorgiou, Vasile Staicu

We consider a nonlinear periodic problem driven by a nonhomogeneous differential operator plus an indefinite potential and a reaction having the competing effects of concave and convex terms. For the superlinear (concave) term we do not employ the usual in such cases Ambrosetti-Rabinowitz condition. Using variational methods together with truncation, perturbation and comparison techniques, we prove a bifurcation-type theorem describing the set of positive solutions as the parameter varies.

Submitted September 29, 2014. Published April 16, 2015.
Math Subject Classifications: 34B15, 34B18, 34C25.
Key Words: Nonhomogeneous differential operator; positive solution; local minimizer; nonlinear maximum principle; mountain pass theorem; bifurcation.

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Sergiu Aizicovici
Department of Mathematics, Ohio University
Athens, OH 45701, USA
email: aizicovs@ohio.edu
  Nikolaos S. Papageorgiou
Department of Mathematics
National Technical University
Zografou Campus, Athens 15780, Greece
email: npapg@math.ntua.gr
Vasile Staicu
Department of Mathematics
CIDMA, University of Aveiro
Campus Universitário de Santiago
3810-193 Aveiro, Portugal
email: vasile@ua.pt

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