scholarly journals Multiplicity of solutions for quasilinear elliptic problems involving Φ -Laplacian operator and critical growth

2019 ◽  
pp. 1-15
Author(s):  
Xuewei Li ◽  
Gao Jia
Keyword(s):  
Elliptic Problems ◽  
Critical Growth ◽  
Laplacian Operator ◽  
Multiplicity Of Solutions ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

scholarly journals Positive solutions of critical quasilinear elliptic problems in general domains

1998 ◽  
Vol 3 (1-2) ◽  
pp. 65-84 ◽  
Author(s):  
Filippo Gazzola
Keyword(s):  
Positive Solutions ◽  
Elliptic Equations ◽  
Elliptic Problems ◽  
Unbounded Domains ◽  
Critical Growth ◽  
Quasilinear Elliptic Equations ◽  
Existence Of Positive Solutions ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

We consider a certain class of quasilinear elliptic equations with a term in the critical growth range. We prove the existence of positive solutions in bounded and unbounded domains. The proofs involve several generalizations of standard variational arguments.

scholarly journals Multiple Solutions for the p(x)− Laplace Operator with Critical Growth

2011 ◽  
Vol 11 (1) ◽  
Author(s):  
Analia Silva
Keyword(s):  
Elliptic Equation ◽  
Laplace Operator ◽  
Multiple Solutions ◽  
Variable Exponent ◽  
Quasilinear Elliptic Equation ◽  
Critical Growth ◽  
Nontrivial Solutions ◽  
Multiplicity Of Solutions ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

AbstractThe aim of this paper is to extend previous results regarding the multiplicity of solutions for quasilinear elliptic problems with critical growth to the variable exponent case. We prove, in the spirit of [4], the existence of at least three nontrivial solutions to the quasilinear elliptic equation −Δ

scholarly journals Anisotropic 1-Laplacian problems with unbounded weights

2021 ◽  
Vol 28 (6) ◽  
Author(s):  
Juan C. Ortiz Chata ◽  
Marcos T. O. Pimenta ◽  
Sergio Segura de León
Keyword(s):  
Bounded Variation ◽  
Mountain Pass Theorem ◽  
Elliptic Problems ◽  
Mountain Pass ◽  
Weighted Spaces ◽  
Laplacian Operator ◽  
Functions Of Bounded Variation ◽  
Quasilinear Elliptic Problems ◽  
Quasilinear Elliptic

AbstractIn this work we prove the existence of nontrivial bounded variation solutions to quasilinear elliptic problems involving a weighted 1-Laplacian operator. A key feature of these problems is that weights are unbounded. One of our main tools is the well-known Caffarelli-Kohn-Nirenberg’s inequality, which is established in the framework of weighted spaces of functions of bounded variation (and that provides us the necessary embeddings between weighted spaces). Additional tools are suitable variants of the Mountain Pass Theorem as well as an extension of the pairing theory by Anzellotti to this new setting.

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