Entropy solution for nonlinear elliptic problem involving variable exponent and Fourier type boundary condition

2011 ◽  
Vol 23 (2) ◽  
pp. 205-228 ◽  
Author(s):  
Ismael Nyanquini ◽  
Stanislas Ouaro
Keyword(s):  
Boundary Condition ◽  
Elliptic Problem ◽  
Variable Exponent ◽  
Entropy Solution ◽  
Nonlinear Elliptic Problem ◽  
Nonlinear Elliptic ◽  
Type Boundary ◽  
Fourier Type ◽  
Type Boundary Condition

scholarly journals Existence result for a nonlinear elliptic problem by topological degree in Sobolev spaces with variable exponent

2021 ◽  
Vol 7 (1) ◽  
pp. 50-65
Author(s):  
Mustapha Ait Hammou ◽  
Elhoussine Azroul
Keyword(s):  
Sobolev Spaces ◽  
Elliptic Problem ◽  
Topological Degree ◽  
Variable Exponent ◽  
Existence Of Solutions ◽  
Nonlinear Elliptic Problem ◽  
Technical Approach ◽  
Nonlinear Elliptic ◽  
Variable Exponent Sobolev Spaces ◽  
Topological Degree Method

AbstractThe aim of this paper is to establish the existence of solutions for a nonlinear elliptic problem of the form\left\{ {\matrix{{A\left( u \right) = f} \hfill & {in} \hfill & \Omega \hfill \cr {u = 0} \hfill & {on} \hfill & {\partial \Omega } \hfill \cr } } \right.where A(u) = −diva(x, u, ∇u) is a Leray-Lions operator and f ∈ W−1,p′(.)(Ω) with p(x) ∈ (1, ∞). Our technical approach is based on topological degree method and the theory of variable exponent Sobolev spaces.

scholarly journals Symmetric Solutions of a Nonlinear Elliptic Problem with Neumann Boundary Condition

2012 ◽  
Vol 03 (11) ◽  
pp. 1686-1688
Author(s):  
Ana Magnolia Marin Ramirez ◽  
Ruben Dario Ortiz Ortiz ◽  
Joel Arturo Rodriguez Ceballos
Keyword(s):  
Boundary Condition ◽  
Elliptic Problem ◽  
Neumann Boundary Condition ◽  
Neumann Boundary ◽  
Nonlinear Elliptic Problem ◽  
Nonlinear Elliptic

scholarly journals A Sub-Supersolution Approach for Robin Boundary Value Problems with Full Gradient Dependence

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 658 ◽  
Author(s):  
Dumitru Motreanu ◽  
Angela Sciammetta ◽  
Elisabetta Tornatore
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Elliptic Problem ◽  
Robin Boundary Condition ◽  
Convection Term ◽  
Nonlinear Elliptic Problem ◽  
Existence Of A Solution ◽  
Nonlinear Elliptic ◽  
Robin Boundary

The paper investigates a nonlinear elliptic problem with a Robin boundary condition, which exhibits a convection term with full dependence on the solution and its gradient. A sub- supersolution approach is developed for this type of problems. The main result establishes the existence of a solution enclosed in the ordered interval formed by a sub-supersolution. The result is applied to find positive solutions.

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