Upper and lower solutions for a superlinear singular boundary value problem

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.

TRIPLE SOLUTIONS FOR NONLINEAR SINGULAR m-POINT BOUNDARY VALUE PROBLEM

In this paper, we study the existence of three solutions to the following nonlinear m-point boundary value problem  u′′(t) + βu(t) = h(t)f(t, u(t)), 0 < t < 1, u′(0) = 0, u(1) = m−2 ∑ i=1 αiu(ηi), where 0 < β < π2 , f ∈ C([0, 1] × R ,R). h(t) is allowed to be singular at t = 0 and t = 1. The arguments are based only upon the Leggett-Williams fixed point theorem. We also prove nonexist results.

An Existence Result of Positive Solutions for Singular Superlinear Boundary Value Problems and Its Applications

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...

Upper and lower solutions method and a fractional differential equation boundary value problem

The method of lower and upper solutions for fractional differential equationDu(t)+ g(t, u(t)) = 0, t ∈ (0, 1), 1 < δ ≤ 2, with Dirichlet boundary condition u(0) = a, u(1) = b is used to give sufficient conditions for the existence of at least one solution.