Resonance problems for p-Laplacian

We study the existence of the weak solution of the nonlinear boundary value problem −(|u′| p−2u′)′=λ|u| p−2u+g(u)−h(x) in (0,π), u(0)=u(π)=0, where p and λ are real numbers, p>1, h∈ L p′ (0, π)( p′= p/( p−1)) and the nonlinearity g: R→ R is a continuous function of the Landesman–Lazer type. Our r...

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Bibliographic Details
Published in:Mathematics and computers in simulation 2003-01, Vol.61 (3), p.599-604
Main Author: Bouchala, Jiřı́
Format: Article
Language:English
Subjects:
Landesman–Lazer type conditions
Resonance at the eigenvalues
The p-Laplacian
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Summary:We study the existence of the weak solution of the nonlinear boundary value problem −(|u′| p−2u′)′=λ|u| p−2u+g(u)−h(x) in (0,π), u(0)=u(π)=0, where p and λ are real numbers, p>1, h∈ L p′ (0, π)( p′= p/( p−1)) and the nonlinearity g: R→ R is a continuous function of the Landesman–Lazer type. Our results generalize previously published results about the solvability of our problem.
ISSN:0378-4754
1872-7166
DOI:10.1016/S0378-4754(02)00139-8