TY - JOUR
T1 - Sub- and super-solutions method for some quasilinear elliptic operators
AU - Unai, Akihito
PY - 2016/3/1
Y1 - 2016/3/1
N2 - In this paper, we shall prove an existence theorem of weak solutions for some quasilinear elliptic equations involving monotone operators which is not necessarily of potential type. Our existence theorem is a natural generalization of the following well-known semilinear problem: −div(M (x)∇u) = g(u) + ƒ in Ω, with Dirichlet boundary condition. The proof is based on the sub- and super-solutions method.
AB - In this paper, we shall prove an existence theorem of weak solutions for some quasilinear elliptic equations involving monotone operators which is not necessarily of potential type. Our existence theorem is a natural generalization of the following well-known semilinear problem: −div(M (x)∇u) = g(u) + ƒ in Ω, with Dirichlet boundary condition. The proof is based on the sub- and super-solutions method.
KW - Monotone operator
KW - Quasilinear elliptic problems
KW - Sub- and super-solutions
UR - http://www.scopus.com/inward/record.url?scp=84959203642&partnerID=8YFLogxK
U2 - 10.17654/MS099060851
DO - 10.17654/MS099060851
M3 - Article
AN - SCOPUS:84959203642
SN - 0972-0871
VL - 99
SP - 851
EP - 867
JO - Far East Journal of Mathematical Sciences
JF - Far East Journal of Mathematical Sciences
IS - 6
ER -