Triple positive solutions for a second order m-point boundary value problem with a delayed argument

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 ...

Triple positive solutions for second-order four-point boundary value problem with sign changing nonlinearities

In this paper, we study the existence of triple positive solutions for second-order four-point boundary value problem with sign changing nonlinearities. We first study the associated Green’s function and obtain some useful properties. Our main tool is the fixed point theorem due to Avery and Peterson. The results of this paper are new and extent previously known results. 2000 Mathematics Subjec...

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

Existence of positive solutions for fourth-order boundary value problems with three- point boundary conditions

In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime pri...

Twin positive solutions of second-order m-point boundary value problem with sign changing nonlinearities

In this paper, we study second-order m-point boundary value problem { u′′(t) + a(t)u′(t) + f(t, u) = 0, 0 ≤ t ≤ 1, u′(0) = 0, u(1) = ∑k i=1 aiu(ξi)− ∑m−2 i=k+1 aiu(ξi), where ai > 0(i = 1, 2, · · ·m − 2), 0 < ∑k i=1 ai − ∑m−2 i=k+1 ai < 1, 0 < ξ1 < ξ2 < · · · < ξm−2 < 1, a ∈ C([0, 1], (−∞, 0)) and f is allowed to change sign. We show that there exist two positive solutions by using Leggett-Will...