A bifurcation-type theorem for the positive solutions of a nonlinear Neumann problem with concave and convex terms

  • Dimitrie Kravvaritis
  • Nikolaus S. Papageorgiou
  • George Smyrlis
Keywords: C-condition, Nonlinear maximum principle, Local minimizers, p-Laplacian, Bifurcation type theorem.


We consider a nonlinear elliptic Neumann problem driven by the p-Laplacian with a reaction that involves the combined effects of a “concave” and of a “convex” terms. The convex term (p-superlinear term) need not satisfy the Ambrosetti-Rabinowitz condition. Employing variational methods based on the critical point theory together with truncation techniques, we prove a bifurcation type theorem for the equation.