Some maximum principles for nonlinear elliptic boundary-value problems

Maximum Principles for a Class of Nonlinear Second-order Elliptic Boundary Value Problems in Divergence Form

For a class of nonlinear elliptic boundary value problems in divergence form, we construct some general elliptic inequalities for appropriate combinations of u(x) and |∇u|2, where u(x) are the solutions of our problems. From these inequalities, we derive, using Hopf ’s maximum principles, some maximum principles for the appropriate combinations of u(x) and |∇u|2, and we list a few examples of p...

Boundary Value Problems for some Fully Nonlinear Elliptic Equations

Let (M, g) be a compact Riemannian manifold of dimension n ≥ 3 with boundary ∂M . We denote the Ricci curvature, scalar curvature, mean curvature, and the second fundamental form by Ric, R , h, and Lαβ , respectively. The Yamabe problem for manifolds with boundary is to find a conformal metric ĝ = eg such that the scalar curvature is constant and the mean curvature is zero. The boundary is call...

Nonlinear Elliptic Boundary Value Problems

It is the object of the present note to present a new nonlinear version of the orthogonal projection method for proving the existence of solutions of nonlinear elliptic boundary value problems. The key point in this method is the application of a new general theorem concerning the solvability of nonlinear functional equations in a reflexive Banach space involving operators which may not be cont...

On discrete maximum principles for nonlinear elliptic problems

Maximum Principles for a Family of Nonlocal Boundary Value Problems

The disconjugacy theory for forward difference equations was developed by Hartman [15] in a landmark paper which has generated so much activity in the study of difference equations. Sturm theory for a second-order finite difference equation goes back to Fort [12], which also serves as an excellent reference for the calculus of finite differences. Hartman considers the nth-order linear finite di...