scholarly journals Some class of nonlinear inequalities with gradient constraints in Orlicz spaces

2020 ◽  
Vol 6 (2) ◽  
pp. 281-302
Author(s):  
S. Ajagjal ◽  
D. Meskine
Keyword(s):  
Existence Of Solutions ◽  
Orlicz Spaces ◽  
Gradient Constraint ◽  
Gradient Constraints

AbstractIn the present paper, we show the existence of solutions of some nonlinear inequalities of the form 〈Au + g(x, u,∇ u), v −u〉 ≥〈 f, v −u〉 with gradient constraint that depend on the solution itself, where A is a Leray-Lions operator defined on Orlicz spaces, g is a nonlinearity and f ∈ L1.

scholarly journals Existence of solutions for some strongly nonlinear parabolic problems involving lower order terms in divergence form in Musielak-Orlicz spaces

2019 ◽  
Vol 38 (6) ◽  
pp. 99-126
Author(s):  
Abdeslam Talha ◽  
Abdelmoujib Benkirane
Keyword(s):  
Lower Order ◽  
Parabolic Equations ◽  
Existence Of Solutions ◽  
Orlicz Spaces ◽  
Nonlinear Parabolic Equations ◽  
Parabolic Problems ◽  
Strongly Nonlinear ◽  
L1 Data ◽  
Nonlinear Parabolic ◽  
Lower Order Terms

In this work, we prove an existence result of entropy solutions in Musielak-Orlicz-Sobolev spaces for a class of nonlinear parabolic equations with two lower order terms and L1-data.

scholarly journals On Degenerate Parabolic Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-7
Author(s):  
Mohammed Kbiri Alaoui
Keyword(s):  
Parabolic Equations ◽  
Existence Of Solutions ◽  
Orlicz Spaces ◽  
Type Equation ◽  
Degenerate Parabolic Equations ◽  
Degenerate Parabolic

The paper deals with the existence of solutions of some generalized Stefan-type equation in the framework of Orlicz spaces.

On the existence of solutions for quadratic integral equations in Orlicz spaces

2016 ◽  
Vol 66 (6) ◽  
Author(s):  
Mieczysław Cichoń ◽  
Mohamed M. A. Metwali
Keyword(s):  
Integral Equations ◽  
Existence Of Solutions ◽  
Orlicz Spaces ◽  
Quadratic Integral ◽  
Quadratic Integral Equations

AbstractWe study quadratic integral equations in Orlicz spaces on the interval [

scholarly journals Existence of a weak bounded solution for nonlinear degenerate elliptic equations in Musielak-Orlicz spaces

2020 ◽  
Vol 6 (1) ◽  
pp. 16-33 ◽  
Author(s):  
M. Bourahma ◽  
J. Bennouna ◽  
M. El Moumni
Keyword(s):  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Bounded Solution ◽  
Orlicz Spaces ◽  
Nonlinear Elliptic Equations ◽  
Degenerate Elliptic Equations ◽  
Nonlinear Elliptic ◽  
Degenerate Elliptic ◽  
Nonlinear Degenerate

AbstractIn this paper, we show the existence of solutions for the nonlinear elliptic equations of the form\left\{ {\matrix{ { - {\rm{div}}\,a\left( {x,u,\nabla u} \right) = f,} \hfill \cr {u \in W_0^1L\varphi \left( \Omega \right) \cap {L^\infty }\left( \Omega \right),} \hfill \cr } } \right.where a\left( {x,s,\xi } \right) \cdot \xi \ge \bar \varphi _x^{ - 1}\left( {\varphi \left( {x,h\left( {\left| s \right|} \right)} \right)} \right)\varphi \left( {x,\left| \xi \right|} \right) and h : ℝ+→]0, 1] is a continuous decreasing function with unbounded primitive. The second term f belongs to LN(Ω) or to Lm(Ω), with m = {{rN} \over {r + 1}} for some r > 0 and φ is a Musielak function satisfying the Δ2-condition.

scholarly journals Strongly nonlinear elliptic unilateral problems without sign condition and with free obstacle in Musielak-Orlicz spaces

2021 ◽  
Vol 55 (1) ◽  
pp. 43-70
Author(s):  
Abdeslam Talha ◽  
Mohamed Saad Bouh Elemine Vall
Keyword(s):  
Nonlinear Term ◽  
Existence Of Solutions ◽  
Orlicz Spaces ◽  
Growth Conditions ◽  
Strongly Nonlinear ◽  
Nonlinear Elliptic ◽  
Sign Condition ◽  
Unilateral Problems ◽  
Sign Conditions ◽  
Lower Order Terms

In this paper, we prove the existence of solutions to an elliptic problem containing two lower order terms, the first nonlinear term satisfying the growth conditions and without sign conditions and the second is a continuous function on R.

scholarly journals Existence of solutions for elliptic equations having natural growth terms in Orlicz spaces

2004 ◽  
Vol 2004 (12) ◽  
pp. 1031-1045 ◽  
Author(s):  
A. Elmahi ◽  
D. Meskine
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equation ◽  
Existence Result ◽  
Existence Of Solutions ◽  
Orlicz Spaces ◽  
Natural Growth ◽  
Strongly Nonlinear ◽  
Nonlinear Elliptic ◽  
Natural Growth Terms

Existence result for strongly nonlinear elliptic equation with a natural growth condition on the nonlinearity is proved.

scholarly journals On Elliptic Equations in Orlicz Spaces Involving Natural Growth Term and Measure Data

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Mohammed Kbiri Alaoui
Keyword(s):  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Orlicz Spaces ◽  
Measure Data ◽  
Natural Growth ◽  
Right Hand

The paper deals with the existence of solutions of elliptic equations in the framework of Orlicz spaces with right-hand side measure and natural growth term.

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