Positive solutions of a second-order nonlinear Robin problem involving the first-order derivative

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...

Positive Solutions of a Nonlinear Higher Order Boundary-value Problem

The authors consider the higher order boundary-value problem u(t) = q(t)f(u(t)), 0 ≤ t ≤ 1, u(i−1)(0) = u(n−2)(p) = u(n−1)(1) = 0, 1 ≤ i ≤ n− 2, where n ≥ 4 is an integer, and p ∈ (1/2, 1) is a constant. Sufficient conditions for the existence and nonexistence of positive solutions of this problem are obtained. The main results are illustrated with an example.

Positive Solutions to a Singular Second Order Boundary Value Problem

In this paper, we establish some criteria for the existence of positive solutions for certain two point boundary value problems for the singular nonlinear second order equation −(ru ) + qu = λf (t, u ) on a time scale T. As a special case when T = R, our results include those of Erbe and Mathsen [11]. Our results are new in a general time scale setting and can be applied to difference and q-dif...

Positive Solutions to a Second-Order Discrete Boundary Value Problem

Throughout Positive Solutions of Second-order Nonlinear Differential Equations

In this paper, we consider the second-order nonlinear and the nonlinear neutral functional differential equations (a(t)x′(t))′ + f(t, x(g(t))) = 0, t ≥ t0 (a(t)(x(t)− p(t)x(t− τ))′)′ + f(t, x(g(t))) = 0, t ≥ t0 . Using the Banach contraction mapping principle, we obtain the existence of throughout positive solutions for the above equations.