scholarly journals On the solvability of nonlinear elliptic equations in Sobolev spaces

1992 ◽  
Vol 56 (2) ◽  
pp. 149-156
Author(s):  
Piotr Fijałkowski
Keyword(s):  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Nonlinear Elliptic

scholarly journals Existence and uniqueness of solutions for a class of degenerate nonlinear elliptic equations

2016 ◽  
Vol 70 (2) ◽  
pp. 9
Author(s):  
Albo Carlos Cavalheiro
Keyword(s):  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Weighted Sobolev Spaces ◽  
Nonlinear Elliptic Equations ◽  
Uniqueness Of Solutions ◽  
Nonlinear Elliptic

In this work we are interested in the existence and uniqueness of solutions for the Navier problem associated to the degenerate nonlinear elliptic equations \begin{align} {\Delta}(v(x)\, {\vert{\Delta}u\vert}^{p-2}{\Delta}u) &-\sum_{j=1}^n D_j{\bigl[}{\omega}_1(x) \mathcal{A}_j(x, u, {\nabla}u){\bigr]}+ b(x,u,{\nabla}u)\, {\omega}_2(x)\\ & = f_0(x) - \sum_{j=1}^nD_jf_j(x), \ \ {\rm in } \ \ {\Omega} \end{align} in the setting of the weighted Sobolev spaces.

scholarly journals On a nonlinear elliptic problems having large monotonocity with L1-data in weighted Orlicz-Sobolev spaces

2019 ◽  
Vol 5 (1) ◽  
pp. 104-116
Author(s):  
Badr El Haji ◽  
Mostafa El Moumni ◽  
Khaled Kouhaila
Keyword(s):  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Entropy Solution ◽  
Elliptic Problems ◽  
Nonlinear Elliptic Equations ◽  
Monotonicity Condition ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic ◽  
Right Hand ◽  
L1 Data

AbstractWe prove in weighted Orlicz-Sobolev spaces, the existence of entropy solution for a class of nonlinear elliptic equations of Leray-Lions type, with large monotonicity condition and right hand side f ∈ L1(Ω).

scholarly journals Nontrivial Solution for a Nonlocal Elliptic Transmission Problem in Variable Exponent Sobolev Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Bilal Cekic ◽  
Rabil A. Mashiyev
Keyword(s):  
Nontrivial Solution ◽  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Variable Exponent ◽  
Nonlinear Elliptic Equations ◽  
Transmission Problem ◽  
Variational Techniques ◽  
Nonlinear Elliptic ◽  
Variable Exponent Sobolev Spaces ◽  
Nonstandard Growth Condition

In this paper, by means of adequate variational techniques and the theory of the variable exponent Sobolev spaces, we show the existence of nontrivial solution for a transmission problem given by a system of two nonlinear elliptic equations ofp(x)-Kirchhoff type with nonstandard growth condition.

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