A multiplicity of solutions for a nonlinear degenerate problem involving a p(x)-Laplace-type operator

2010 ◽  
Vol 55 (5-6) ◽  
pp. 417-429 ◽  
Author(s):  
Olfa Allegue ◽  
Mounir Bezzarga
Keyword(s):  
Type Operator ◽  
Degenerate Problem ◽  
Multiplicity Of Solutions ◽  
Laplace Type ◽  
Nonlinear Degenerate

scholarly journals A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids

2006 ◽  
Vol 462 (2073) ◽  
pp. 2625-2641 ◽  
Author(s):  
Mihai Mihăilescu ◽  
Vicenţiu Rădulescu
Keyword(s):  
Boundary Value Problem ◽  
Sobolev Spaces ◽  
Variable Exponent ◽  
Electrorheological Fluids ◽  
Mountain Pass Lemma ◽  
Multiplicity Result ◽  
Smooth Bounded Domain ◽  
Degenerate Problem ◽  
Laplace Type ◽  
Nonlinear Degenerate

We study the boundary value problem in , u =0 on , where is a smooth bounded domain in and is a -Laplace type operator, with . We prove that if λ is large enough then there exist at least two non-negative weak solutions. Our approach relies on the variable exponent theory of generalized Lebesgue–Sobolev spaces, combined with adequate variational methods and a variant of the Mountain Pass lemma.

HEAT KERNEL ASYMPTOTICS FOR ROOTS OF GENERALIZED LAPLACIANS

2003 ◽  
Vol 14 (04) ◽  
pp. 397-412 ◽  
Author(s):  
CHRISTIAN BÄR ◽  
SERGIU MOROIANU
Keyword(s):  
Heat Kernel ◽  
Closed Manifold ◽  
Type Operator ◽  
Wodzicki Residue ◽  
Heat Trace ◽  
Heat Kernel Asymptotics ◽  
Laplace Type

We describe the heat kernel asymptotics for roots of a Laplace type operator Δ on a closed manifold. A previously known relation between the Wodzicki residue of Δ and heat trace asymptotics is shown to hold pointwise for the corresponding densities.

scholarly journals Entropy solutions for an adaptive fourth-order nonlinear degenerate problem for noise removal

2021 ◽  
Vol 6 (4) ◽  
pp. 3974-3995
Author(s):  
Abdelgader Siddig ◽  
◽  
Zhichang Guo ◽  
Zhenyu Zhou ◽  
Boying Wu ◽  
...  
Keyword(s):  
Fourth Order ◽  
Noise Removal ◽  
Entropy Solutions ◽  
Degenerate Problem ◽  
Nonlinear Degenerate

scholarly journals Multiplicity of solutions to discrete inclusions with the p(k)-Laplace type equations

2018 ◽  
Vol 5 (1) ◽  
pp. 76-88
Author(s):  
Stanislas Ouaro ◽  
Malick Zoungrana
Keyword(s):  
Critical Points ◽  
Three Solutions ◽  
Multiplicity Of Solutions ◽  
Lipschitz Continuous ◽  
Three Critical Points Theorem ◽  
Existence And Multiplicity ◽  
Locally Lipschitz ◽  
Laplace Type ◽  
Locally Lipschitz Continuous

AbstractIn this article, we prove the existence and multiplicity of solutions to discrete inclusions with the p(k)-Laplace type equations. We are interested in the existence of three solutions with the aid of linking arguments and using a three critical points theorem, for locally Lipschitz continuous fonctions.

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