Strong resonance for some quasilinear elliptic equations

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Abstract

We study the existence of the weak solutions of the nonlinear boundary value problem-Δpu=λ1up-2u+gu-hxin Ω,u=0on ∂Ω,where the nonlinearity g is of the Landesman-Lazer type. Our sufficient conditions generalize all previously published results about the strong resonance at the first eigenvalue. © 2000 Academic Press.

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Bouchala, J., & Drábek, P. (2000). Strong resonance for some quasilinear elliptic equations. Journal of Mathematical Analysis and Applications, 245(1), 7–19. https://doi.org/10.1006/jmaa.2000.6713

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