Existence and multiplicity of solutions for an anisotropic elliptic problem involving variable exponent growth conditions

2010 ◽  
Vol 89 (2) ◽  
pp. 257-271 ◽  
Author(s):  
Mihai Mihăilescu ◽  
Gheorghe Moroşanu
Keyword(s):  
Elliptic Problem ◽  
Variable Exponent ◽  
Growth Conditions ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity

scholarly journals Elliptic problems in variable exponent spaces

2006 ◽  
Vol 74 (2) ◽  
pp. 197-206 ◽  
Author(s):  
Mihai Mihailescu
Keyword(s):  
Variational Principle ◽  
Nonlinear Elliptic Equation ◽  
Variable Exponent ◽  
Mountain Pass Theorem ◽  
Growth Conditions ◽  
Cylindrical Symmetry ◽  
Multiplicity Results ◽  
Variable Exponent Spaces ◽  
Nonlinear Elliptic ◽  
Existence And Multiplicity

In this paper we study a nonlinear elliptic equation involving p(x)-growth conditions on a bounded domain having cylindrical symmetry. We establish existence and multiplicity results using as main tools the mountain pass theorem of Ambosetti and Rabinowitz and Ekeland's variational principle.

scholarly journals Multiple Solutions for a Nonlocal Elliptic Problem Involving p x , q x -Biharmonic Operator

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Qi Zhang ◽  
Qing Miao
Keyword(s):  
Variational Principle ◽  
Elliptic Problem ◽  
Multiple Solutions ◽  
Sufficient Conditions ◽  
Biharmonic Operator ◽  
Type Problem ◽  
Navier Boundary Conditions ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Kirchhoff Type Problem

In this paper, using the variational principle, the existence and multiplicity of solutions for p x , q x -Kirchhoff type problem with Navier boundary conditions are proved. At the same time, the sufficient conditions for the multiplicity of solutions are obtained.

scholarly journals On a Robin type problem involving 𝑝(𝑥)-Laplacian operator

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Abdesslem Ayoujil ◽  
Anass Ourraoui
Keyword(s):  
Variational Approach ◽  
Growth Conditions ◽  
Laplacian Operator ◽  
Robin Problem ◽  
Type Problem ◽  
Multiplicity Results ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Cerami Condition ◽  
Weaker Conditions

Abstract This paper deals with the existence and multiplicity of solutions for the p ⁢ ( x ) p(x) -Laplacian Robin problem without the well-known Ambrosetti–Rabinowitz type growth conditions. By means of the variational approach (with the Cerami condition), existence and multiplicity results of solutions are established under weaker conditions.

scholarly journals Existence and Multiplicity of Solutions for Sublinear Schrödinger Equations with Coercive Potentials

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Dong-Lun Wu
Keyword(s):  
Growth Conditions ◽  
Schrodinger Equations ◽  
Linking Theorem ◽  
Infinitely Many Solutions ◽  
Schrödinger Equations ◽  
Fountain Theorem ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Working Space ◽  
Variant Fountain Theorem

In this study, we consider the following sublinear Schrödinger equations −Δu+Vxu=fx,u,for x∈ℝN,ux⟶0,asu⟶∞, where fx,u satisfies some sublinear growth conditions with respect to u and is not required to be integrable with respect to x. Moreover, V is assumed to be coercive to guarantee the compactness of the embedding from working space to LpℝN for all p∈1,2∗. We show that the abovementioned problem admits at least one solution by using the linking theorem, and there are infinitely many solutions when fx,u is odd in u by using the variant fountain theorem.

scholarly journals EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A NEUMANN PROBLEM INVOLVING VARIABLE EXPONENT GROWTH CONDITIONS

2008 ◽  
Vol 50 (3) ◽  
pp. 565-574 ◽  
Author(s):  
MARIA-MAGDALENA BOUREANU ◽  
MIHAI MIHĂILESCU
Keyword(s):  
Boundary Condition ◽  
Elliptic Equation ◽  
Neumann Problem ◽  
Neumann Boundary Condition ◽  
Variable Exponent ◽  
Main Tool ◽  
Neumann Boundary ◽  
Growth Conditions ◽  
Linear Elliptic Equation ◽  
Existence And Multiplicity

AbstractIn this paper we study a non-linear elliptic equation involving p(x)-growth conditions and satisfying a Neumann boundary condition on a bounded domain. For that equation we establish the existence of two solutions using as a main tool an abstract linking argument due to Brézis and Nirenberg.

scholarly journals Multiplicity of solutions for a class of quasilinear problem in exterior domains with Neumann conditions

2004 ◽  
Vol 2004 (3) ◽  
pp. 251-268 ◽  
Author(s):  
Claudianor O. Alves ◽  
Paulo C. Carrião ◽  
Everaldo S. Medeiros
Keyword(s):  
Boundary Conditions ◽  
Elliptic Problem ◽  
Exterior Domain ◽  
Neumann Boundary ◽  
Exterior Domains ◽  
Multiplicity Of Solutions ◽  
Quasilinear Elliptic Problem ◽  
Existence And Multiplicity ◽  
Quasilinear Problem ◽  
Quasilinear Elliptic

We study the existence and multiplicity of solutions for a class of quasilinear elliptic problem in exterior domain with Neumann boundary conditions.

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