Resonant Robin problems with indefinite and unbounded potential

Nikolaos S. Papageorgiou, George Smyrlis



We study a semilinear Robin problem with an indefinite and unbounded potential and a reaction term which asymptotically at $ \pm \infty $ is resonant with respect to any nonprincipal nonnegative eigenvalue. We prove two multiplicity theorems producing three and four nontrivial solutions respectively. Our approach uses variational methods based on the critical point theory, truncation and perturbation techniques, and Morse theory (critical groups).


Indefinite and unbounded potential; resonance; Robin boundary condition; maximum principle; critical groups; multiple solutions

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