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2018 Multiplicity of solutions for $p$-biharmonic problems with critical growth
H. Bueno, L. Paes-Leme, H. Rodrigues
Rocky Mountain J. Math. 48(2): 425-442 (2018). DOI: 10.1216/RMJ-2018-48-2-425

Abstract

We prove the existence of infinitely many solutions for $p$-biharmonic problems in a bounded, smooth domain $\Omega $ with concave-convex nonlinearities dependent upon a parameter $\lambda $ and a positive continuous function $f\colon \overline {\Omega }\to \mathbb {R}$. We simultaneously handle critical case problems with both Navier and Dirichlet boundary conditions by applying the Ljusternik-Schnirelmann method. The multiplicity of solutions is obtained when $\lambda $ is small enough. In the case of Navier boundary conditions, all solutions are positive, and a regularity result is proved.

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H. Bueno. L. Paes-Leme. H. Rodrigues. "Multiplicity of solutions for $p$-biharmonic problems with critical growth." Rocky Mountain J. Math. 48 (2) 425 - 442, 2018. https://doi.org/10.1216/RMJ-2018-48-2-425

Information

Published: 2018
First available in Project Euclid: 4 June 2018

zbMATH: 06883474
MathSciNet: MR3810206
Digital Object Identifier: 10.1216/RMJ-2018-48-2-425

Subjects:
Primary: 35J35, 35J40, 35J91

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 2 • 2018
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