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In the present paper, our purpose is to construct the Fučik spectrum Cl±$C_{l}^{\pm}$ (cf. (2.13) and (2.17) below) with different weights for the p-Laplacian. As an application, we will discuss the existence of nontrivial solutions to the p-Laplace equations with resonance on the Fučik spectrum by making use of variational methods and Morse theory.

The Fučik spectrum of the p-Laplace equations with different weights and its resonance problems