Triple solutions for nonlinear singular m-point boundary value problem

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.

Triple positive solutions of $m$-point boundary value problem on time scales with $p$-Laplacian

‎In this paper‎, ‎we consider the multipoint boundary value problem for one-dimensional $p$-Laplacian‎ ‎dynamic equation on time scales‎. ‎We prove the existence at least three positive solutions of the boundary‎ ‎value problem by using the Avery and Peterson fixed point theorem‎. ‎The interesting point is that the non-linear term $f$ involves a first-order derivative explicitly‎. ‎Our results ...

Existence of triple positive solutions for boundary value problem of nonlinear fractional differential equations

This article is devoted to the study of existence and multiplicity of positive solutions to a class of nonlinear fractional order multi-point boundary value problems of the type−Dq0+u(t) = f(t, u(t)), 1 < q ≤ 2, 0 < t < 1,u(0) = 0, u(1) =m−2∑ i=1δiu(ηi),where Dq0+ represents standard Riemann-Liouville fractional derivative, δi, ηi ∈ (0, 1) withm−2∑i=1δiηi q−1 < 1, and f : [0, 1] × [0, ∞) → [0, ...

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

Nontrivial Solutions for Singular Nonlinear Three-Point Boundary Value Problems

The singular nonlinear three-point boundary value problems { −(Lu)(t) = h(t)f (u(t)), 0 < t < 1, βu(0)− γ u′(0) = 0, u(1) = αu(η) are discussed under some conditions concerning the first eigenvalue corresponding to the relevant linear operator, where (Lu)(t) = (p(t)u′(t))′+q(t)u(t), 0 < η < 1, h(t) is allowed to be singular at both t = 0 and t = 1, and f need not be nonnegative. The associated ...