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.

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.

ON THE ASYMPTOTIC BEHAVIOUR OF THE SOLUTION OF ELLIPTIC PROBLEMS IN CYLINDRICAL DOMAINS BECOMING UNBOUNDED

2002 ◽  
Vol 04 (01) ◽  
pp. 15-44 ◽  
Author(s):  
M. CHIPOT ◽  
A. ROUGIREL
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Behaviour ◽  
Cross Section ◽  
Elliptic Problems ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic ◽  
Cylindrical Domains ◽  
Linear And Nonlinear ◽  
The Cross

We study the asymptotic behavior of the solution of linear and nonlinear elliptic problems in cylindrical domains becoming unbounded in one or several directions. In particular we show that this solution converges in H1 norm toward the solution of problems set on the cross section of the domains.

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