A characteristic initial boundary value problem for a symmetric positive system

A characteristic initial value problem for a strictly hyperbolic system

Consider the system Autt +Cuxx = f(x,t), (x,t) ∈ T for u(x,t) in R2, where A and C are real constant 2× 2 matrices, and f is a continuous function in R2. We assume that detC ≠ 0 and that the system is strictly hyperbolic in the sense that there are four distinct characteristic curves Γi, i= 1, . . . ,4, in xt-plane whose gradients (ξ1i,ξ2i) satisfy det[Aξ2 1i+ Cξ2 2i]= 0. We allow the character...

Triple Positive Symmetric Solutions for a Lidstone Boundary Value Problem

In this paper, we consider the Lidstone boundary value problem (−1)y = f(y(t)), 0 ≤ t ≤ 1, y(0) = 0 = y(1), 0 ≤ i ≤ m − 1, where f : R→ [0,∞). Growth conditions are imposed on f and inequalities involving the Green’s function for this problem are used which enable us to apply the Leggett-Williams Fixed Point Theorem for cones in ordered Banach spaces. This in turn yields the existence of at lea...

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.

Positive solutions for discrete fractional initial value problem

‎‎In this paper‎, ‎the existence and uniqueness of positive solutions for a class of nonlinear initial value problem for a finite fractional difference equation obtained by constructing the upper and lower control functions of nonlinear term without any monotone requirement‎ .‎The solutions of fractional difference equation are the size of tumor in model tumor growth described by the Gompertz f...

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