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

Author(s):  
H. Sabiki ◽  
H. Moussa ◽  
M. Rhoudaf
1998 ◽  
Vol 41 (2) ◽  
pp. 333-357
Author(s):  
N. Chemetov ◽  
J. F. Rodrigues

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.


2018 ◽  
Vol 36 (1) ◽  
pp. 51
Author(s):  
Mustafa Ait Khellou ◽  
Abdelmoujib Benkirane

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.


2006 ◽  
Vol 2006 ◽  
pp. 1-20 ◽  
Author(s):  
L. Aharouch ◽  
A. Benkirane ◽  
M. Rhoudaf

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).


2011 ◽  
Vol 32 (4) ◽  
pp. 254-269
Author(s):  
Aomar Anane ◽  
Omar Chakrone ◽  
Mohammed Chehabi

2021 ◽  
Vol 55 (1) ◽  
pp. 43-70
Author(s):  
Abdeslam Talha ◽  
Mohamed Saad Bouh Elemine Vall

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.


2018 ◽  
Vol 11 (06) ◽  
pp. 1850079
Author(s):  
H. Moussa ◽  
M. Rhoudaf ◽  
H. Sabiki

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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