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Abstract We consider two types of nonlinear eigenvalue problems involving Laplace and p -Laplace operators (p>2) (p > 2). The main result establishes the existence of at least two nontrivial weak solutions in the case of the perturbed equation and the existence of a continuous spectrum in the case of the (p, 2) -equation. In both cases, variational methods play a central role in our arguments.
Krzysztof Bień (Tue,) studied this question.