Strongly resonant Robin problems with idefinite and unbounded potential
KeywordsIndefinite and unbounded potential, Robin boundary condition, strong resonance, multiple nontrivial solutions, critical groups
AbstractWe consider a Robin boundary value problem driven by the Laplacian plus an indefinite and unbounded potential. We assume that the reaction term of the equation is resonant with respect to the principal eigenvalue and the resonance is strong. Using primarily variational tools we prove two multiplicity theorems producing respectively two and three nontrivial smooth solutions.
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