On a Class of Nonlinear Elliptic Unilateral Problems Involving Only a Growth Condition on Nonlinearities

2020 ◽  
pp. 251-271
Author(s):  
H. Sabiki ◽  
H. Moussa ◽  
M. Rhoudaf
Keyword(s):  
Growth Condition ◽  
Nonlinear Elliptic ◽  
Unilateral Problems

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 Non-linear elliptic unilateral problems in Musielak-Orlicz spaces with L1 data

2018 ◽  
Vol 36 (1) ◽  
pp. 51
Author(s):  
Mustafa Ait Khellou ◽  
Abdelmoujib Benkirane
Keyword(s):  
Sobolev Space ◽  
Existence Result ◽  
Orlicz Spaces ◽  
Conjugate Function ◽  
Natural Growth ◽  
Nonlinear Elliptic ◽  
L1 Data ◽  
Non Linear ◽  
Unilateral Problems ◽  
Natural Growth Terms

We prove an existence result of solutions for nonlinear elliptic unilateral problems having natural growth terms and L1 data in Musielak-Orlicz-Sobolev space W1Lφ, under the assumption that the conjugate function of φ satisfies the ∆2-condition.

scholarly journals Strongly nonlinear elliptic variational unilateral problems in Orlicz space

2006 ◽  
Vol 2006 ◽  
pp. 1-20 ◽  
Author(s):  
L. Aharouch ◽  
A. Benkirane ◽  
M. Rhoudaf
Keyword(s):  
Existence Result ◽  
Order Term ◽  
Natural Growth ◽  
Unilateral Problem ◽  
Strongly Nonlinear ◽  
Nonlinear Elliptic ◽  
Sign Condition ◽  
Carathéodory Function ◽  
Unilateral Problems ◽  
The Right

We will be concerned with the existence result of unilateral problem associated to the equations of the formAu+g(x,u,∇u)=f, whereAis a Leray-Lions operator from its domainD(A)⊂W01LM(Ω)intoW−1EM¯(Ω). On the nonlinear lower order termg(x,u,∇u), we assume that it is a Carathéodory function having natural growth with respect to|∇u|, and satisfies the sign condition. The right-hand sidefbelongs toW−1EM¯(Ω).

Existence of solutions for some nonlinear elliptic unilateral problems having L 1 data

2011 ◽  
Vol 32 (4) ◽  
pp. 254-269
Author(s):  
Aomar Anane ◽  
Omar Chakrone ◽  
Mohammed Chehabi
Keyword(s):  
Existence Of Solutions ◽  
Nonlinear Elliptic ◽  
Unilateral Problems

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.

Existence results for diffusion–convection equations of nonlinear unilateral problems defined in Orlicz–Sobolev spaces

2018 ◽  
Vol 11 (06) ◽  
pp. 1850079
Author(s):  
H. Moussa ◽  
M. Rhoudaf ◽  
H. Sabiki
Keyword(s):  
Elliptic Equations ◽  
Order Term ◽  
Nonlinear Elliptic Equations ◽  
Strongly Nonlinear ◽  
Nonlinear Elliptic ◽  
Polynomial Type ◽  
Carathéodory Function ◽  
Unilateral Problems ◽  
The Right ◽  
Diffusion Convection

We prove the existence result of unilateral problems associated to strongly nonlinear elliptic equations whose model, including the diffusion–convection equation, is [Formula: see text]. We study exactly the following general case [Formula: see text] where [Formula: see text] is a Leray–Lions operator having a growth not necessarily of polynomial type, the lower order term [Formula: see text] : [Formula: see text] is a Carathéodory function, for a.e. [Formula: see text] and for all [Formula: see text] satisfying only a growth condition and the right-hand side [Formula: see text] belongs to [Formula: see text].

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