scholarly journals Compact embeddings for Sobolev spaces of variable exponents and existence of solutions for nonlinear elliptic problems involving the p(x)-Laplacian and its critical exponent

2010 ◽  
Vol 35 ◽  
pp. 115-130 ◽  
Author(s):  
Yoshihiro Mizuta ◽  
Takao Ohno ◽  
Tetsu Shimomura ◽  
Naoki Shioji
Keyword(s):  
Critical Exponent ◽  
Sobolev Spaces ◽  
Existence Of Solutions ◽  
Elliptic Problems ◽  
Variable Exponents ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic ◽  
Compact Embeddings

Existence of solutions for some nonlinear elliptic problems involving Minty’s lemma

2018 ◽  
Vol 68 (2) ◽  
pp. 513-534
Author(s):  
Mohammed Al-Hawmi ◽  
Abdelmoujib Benkirane ◽  
Hassane Hjiaj ◽  
Abdelfattah Touzani
Keyword(s):  
Existence Of Solutions ◽  
Elliptic Problems ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic ◽  
Minty’S Lemma

scholarly journals A class of nonlinear elliptic problems with nonconvex constraints and applications

1998 ◽  
Vol 41 (2) ◽  
pp. 333-357
Author(s):  
N. Chemetov ◽  
J. F. Rodrigues
Keyword(s):  
Existence Of Solutions ◽  
Elliptic Problems ◽  
Monotone Operators ◽  
Global Constraints ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic ◽  
Biological Population ◽  
Unilateral Problems ◽  
Nonlocal Terms ◽  
Nonconvex Constraints

Conditions for the existence of solutions of a class of elliptic problems with nonconvex constraints are given in the general framework of pseudo-monotone operators. Applications are considered in unilateral problems of free boundary type, yielding the solvability of a Reynold's lubrication model and of a biological population problem with nonlocal terms and global constraints.

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 Existence of entropy solutions for some nonlinear problems in Orlicz spaces

2002 ◽  
Vol 7 (2) ◽  
pp. 85-102 ◽  
Author(s):  
A. Benkirane ◽  
J. Bennouna
Keyword(s):  
Sobolev Spaces ◽  
Orlicz Spaces ◽  
Elliptic Problems ◽  
Nonlinear Problems ◽  
Entropy Solutions ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic

We study in the framework of Orlicz Sobolev spacesW01LM(Ω), the existence of entropic solutions to the nonlinear elliptic problems:−div a(x,u,∇u)+div Φ(u)=f in Ω, for the case where the second member of the equationf∈L 1(Ω), andΦ∈(C0(ℝ))N.

Applications of Riccati-type inequalities to asymptotic theory of elliptic problems

2009 ◽  
Vol 139 (5) ◽  
pp. 1071-1089
Author(s):  
Hiroyuki Usami
Keyword(s):  
Asymptotic Behaviour ◽  
Asymptotic Theory ◽  
Existence Of Solutions ◽  
Necessary Conditions ◽  
Elliptic Problems ◽  
Nonlinear Elliptic Problems ◽  
Liouville Type ◽  
One Dimensional ◽  
Nonlinear Elliptic ◽  
Liouville Type Theorems

We show how one-dimensional generalized Riccati-type inequalities can be employed to analyse asymptotic behaviour of solutions of elliptic problems. We give Liouville-type theorems as well as necessary conditions for the existence of solutions of specified asymptotic behaviour of nonlinear elliptic problems.

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