Positive Solutions of a Nonlinear Parabolic Partial Differential Equation

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.

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

Uncountably many bounded positive solutions for a second order nonlinear neutral delay partial difference equation

In this paper we consider the second order nonlinear neutral delay partial difference equation $Delta_nDelta_mbig(x_{m,n}+a_{m,n}x_{m-k,n-l}big)+ fbig(m,n,x_{m-tau,n-sigma}big)=b_{m,n}, mgeq m_{0},, ngeq n_{0}.$Under suitable conditions, by making use of the Banach fixed point theorem, we show the existence of uncountably many bounded positive solutions for the above partial difference equation...

Bifurcation and Stability for a Nonlinear Parabolic Partial Differential Equation

This note is a brief report on some research conducted by the authors in 1971. A complete report on this same research is scheduled to appear in a separate article [2]. Let ƒ be a given function continuously mapping the real line R into itself. Let A be a given nonnegative real number. Let : [0, TT]-+R be any C^-smooth function such that (0)=<£(7r)=0. We shall be discussing the following ...

A Nonlinear Parabolic Partial Differential Equation Model for Image Enhancement

Abstract—We present a robust nonlinear parabolic partial differential equation (PDE)-based denoising scheme in this article. Our approach is based on a second-order anisotropic diffusion model that is described first. Then, a consistent and explicit numerical approximation algorithm is constructed for this continuous model by using the finite-difference method. Finally, our restoration experime...