Geodesic
The Method of Upper and Lower Solutions for Some Nonlinear Boundary Value Problems in Unbounded Domains
Canadian journal of mathematics, Tome 37 (1985) no. 3, pp. 430-441

Voir la notice de l'article provenant de la source Cambridge University Press

Let D be a bounded domain in the Euclidean space R N(N ≦ 2) and let where is the closure of D. We assume that the boundary ∂G of G is smooth. Consider the boundary value problem (abbreviated to BVP in the sequel). (1) (1) where A is a nonlinear elliptic differential operator in divergence form of Leray-Lions type, ∇u = grad u, f is a distribution on G and p(x, t, η) is a function defined on G × R × R N . Among other hypotheses we shall, roughly speaking, assume that p has completely unrelated growth rates in the first and the third variables. In this paper we prove the solvability of the BVP (1), (2) under the assumption that it has both an upper solution ψ and a lower solution φ with φ ≧ ψ. 
Các, Nguyên Phuong. The Method of Upper and Lower Solutions for Some Nonlinear Boundary Value Problems in Unbounded Domains. Canadian journal of mathematics, Tome 37 (1985) no. 3, pp. 430-441. doi: 10.4153/CJM-1985-025-0
@article{10_4153_CJM_1985_025_0,
     author = {C\'ac, Nguy\^en Phuong},
     title = {The {Method} of {Upper} and {Lower} {Solutions} for {Some} {Nonlinear} {Boundary} {Value} {Problems} in {Unbounded} {Domains}},
     journal = {Canadian journal of mathematics},
     pages = {430--441},
     year = {1985},
     volume = {37},
     number = {3},
     doi = {10.4153/CJM-1985-025-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1985-025-0/}
}
TY  - JOUR
AU  - Các, Nguyên Phuong
TI  - The Method of Upper and Lower Solutions for Some Nonlinear Boundary Value Problems in Unbounded Domains
JO  - Canadian journal of mathematics
PY  - 1985
SP  - 430
EP  - 441
VL  - 37
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1985-025-0/
DO  - 10.4153/CJM-1985-025-0
ID  - 10_4153_CJM_1985_025_0
ER  - 
%0 Journal Article
%A Các, Nguyên Phuong
%T The Method of Upper and Lower Solutions for Some Nonlinear Boundary Value Problems in Unbounded Domains
%J Canadian journal of mathematics
%D 1985
%P 430-441
%V 37
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1985-025-0/
%R 10.4153/CJM-1985-025-0
%F 10_4153_CJM_1985_025_0

[1] 1. Các, N. P., Nonlinear elliptic boundary value problems for unbounded domains, J. Differential Equations 45 (1982), 191–198. Google Scholar

[2] 2. Các, N. P., On some quasilinear elliptic boundary value problems with conditions at infinity, J. Differential Equations 52 (1984), 342–355. Google Scholar

[3] 3. Hess, P., Nonlinear elliptic problems in unbounded domains, International Summer School on Nonlinear Operators, Berlin, Sept. 1975, in “Abhandlung der Akademie der Wissenschafter der DDR.“ Google Scholar

[4] 4. Hess, P., A second order nonlinear elliptic boundary value problem, in “Nonlinear Analysis: A collection of papers in honor of Erich H. Rothe,” (Academic Press, New York, 1978). Google Scholar | DOI

[5] 5. Lions, J. L., Quelques méthodes de résolution des problèmes aux limites nonlinéaires (Dunod, Gauthier-Villars, Paris, 1969). Google Scholar

Cité par Sources :