Bounded Positive Solutions for a Third Order Discrete 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...

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...

Existence of positive solutions of a third order nonlinear differential equation with positive and negative terms

Existence of Positive Periodic Solutions for a Third-order Delay Differential Equation

In this paper, the following third-order nonlinear delay differential equation with periodic coefficients x′′′(t) + p(t)x′′(t) + q(t)x′(t) + r(t)x(t) = f (t, x (t) , x(t− τ(t))) + c(t)x′(t− τ(t)), is considered. By employing Green’s function and Krasnoselskii’s fixed point theorem, we state and prove the existence of positive periodic solutions to the third-order delay differential equation.

Positive Solutions for a Singular Third Order Boundary Value Problem

The existence of positive solutions is shown for the third order boundary value problem, u′′′ = f (x,u),0 < x < 1, u(0) = u(1) = u′′(1) = 0, where f (x,y) is singular at x = 0 , x = 1 , y = 0 , and may be singular at y = ∞. The method involves application of a fixed point theorem for operators that are decreasing with respect to a cone. Mathematics subject classification (2010): 34B16, 34B18.