scholarly journals Multiplicity of solutions for anisotropic quasilinear elliptic equations with variable exponents

2010 ◽  
Vol 17 (5) ◽  
pp. 875-889 ◽  
Author(s):  
Denisa Stancu-Dumitru
Keyword(s):  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Variable Exponents ◽  
Multiplicity Of Solutions ◽  
Quasilinear Elliptic

scholarly journals A Picone identity for variable exponent operators and applications

2019 ◽  
Vol 9 (1) ◽  
pp. 327-360 ◽  
Author(s):  
Rakesh Arora ◽  
Jacques Giacomoni ◽  
Guillaume Warnault
Keyword(s):  
Parabolic Equations ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Fast Diffusion ◽  
Variable Exponents ◽  
Uniqueness Results ◽  
Picone Identity ◽  
Weak Comparison Principle ◽  
Quasilinear Elliptic ◽  
Fast Diffusion Equations

Abstract In this work, we establish a new Picone identity for anisotropic quasilinear operators, such as the p(x)-Laplacian defined as div(|∇ u|p(x)−2 ∇ u). Our extension provides a new version of the Diaz-Saa inequality and new uniqueness results to some quasilinear elliptic equations with variable exponents. This new Picone identity can be also used to prove some accretivity property to a class of fast diffusion equations involving variable exponents. Using this, we prove for this class of parabolic equations a new weak comparison principle.

Symmetric And Nonsymmetric Solutions For a Class of Quasilinear Schrödinger Equations

2008 ◽  
Vol 8 (2) ◽  
Author(s):  
Uberlandio B. Severo
Keyword(s):  
Elliptic Equations ◽  
Mountain Pass Theorem ◽  
Mountain Pass ◽  
Quasilinear Elliptic Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Multiplicity Of Solutions ◽  
Principle Of Symmetric Criticality ◽  
Quasilinear Elliptic

AbstractWe use the mountain-pass theorem combined with the principle of symmetric criticality to establish multiplicity of solutions for the class of quasilinear elliptic equations-Δu + V(z)u - Δ(uwhere N ≥ 4, the potential V : ℝ

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