On a nonlinear boundary value problem modeling corneal shape

On a Nonlinear Elliptic Boundary Value Problem

Consider a bounded domain G C R (_N>1) with smooth boundary T . Let L be a uniformly elliptic linear differential operator. Let y and ß be two maximal monotone mappings in R. We prove that, when y ? 2 satisfies a certain growth condition, given f £ L (G ) there is u € H (G) such that Lu + y(u) 3 f a.e. on G, and -du/d v e ß(u\ ) a.e. on T, where du/civ is the conormal derivative associated with...

Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.

On a Boundary Value Problem for Nonlinear Functional Differential Equations

The following notation is used throughout the paper: N is the set of all natural numbers. R is the set of all real numbers, R+ = [0,+∞[,[x]+ = (1/2)(|x|+ x), [x]− = (1/2)(|x|− x). C([a,b];R) is the Banach space of continuous functions u : [a,b]→ R with the norm ‖u‖C =max{|u(t)| : t ∈ [a,b]}. C̃([a,b];R) is the set of absolutely continuous functions u : [a,b]→ R. L([a,b];R) is the Banach space of...

Triple Positive Solutions for Boundary Value Problem of a Nonlinear Fractional Differential Equation

Nonlinear Three Point Boundary Value Problem

In this work, we establish sufficient conditions for the existence of solutions for a three point boundary value problem generated by a third order differential equation. We give sufficient conditions that allow us to obtain the existence of a nontrivial solution. Then by using the Leray Schauder nonlinear alternative we prove the existence of at least one solution of the posed problem. As an a...