Some general concepts of sub- and supersolutions for nonlinear elliptic problems. (English) Zbl 1293.35124

Le, Vy Khoi; Schmitt, Klaus

Topol. Methods Nonlinear Anal. 28, No. 1, 87-103 (2006).

Summary: We propose general and unified concepts of sub- and supersolutions for boundary value problems that encompass several types of boundary conditions for nonlinear elliptic equations and variational inequalities. Various, by now classical, sub- and supersolution existence and comparison results are covered by the general theory presented here.

MSC:

35J87	Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators
35B45	A priori estimates in context of PDEs
35J60	Nonlinear elliptic equations
47H05	Monotone operators and generalizations
47N20	Applications of operator theory to differential and integral equations