Abstract
In this paper, we study the existence of three positive solutions for fourth-order singular nonlocal boundary value problems. We show that there exist triple symmetric positive solutions by using Leggett-Williams fixed-point theorem. The conclusions in this paper essentially extend and improve some known results. MSC: 34B16.
Highlights
Boundary value problems for ordinary differential equations arise in different areas of applied mathematics and physics, the existence of positive solutions for such problems has become an important area of investigation in recent years
A class of boundary value problems with nonlocal boundary conditions appeared in heat conduction, chemical engineering, underground water flow, thermoelasticity, and plasma physics
Motivated by the works mentioned above, in this paper, we study the existence of three symmetric positive solutions for the following fourth-order singular nonlocal boundary value problem(NBVP):
Summary
Boundary value problems for ordinary differential equations arise in different areas of applied mathematics and physics, the existence of positive solutions for such problems has become an important area of investigation in recent years. A class of boundary value problems with nonlocal boundary conditions appeared in heat conduction, chemical engineering, underground water flow, thermoelasticity, and plasma physics. Such problems include two-point, threepoint, multi-point boundary value problems as special cases and have attracted the attention of Gallardo [1], Karakostas and Tsamatos [2], Lomtatidze and Malaguti [3] (and see the references therein). Motivated by the works mentioned above, in this paper, we study the existence of three symmetric positive solutions for the following fourth-order singular nonlocal boundary value problem(NBVP): u′′′′(t)(t) = g(t)f (t, u), 0 < t < 1, u(0). We show that there exist triple symmetric positive solutions by using Leggett-Williams fixed-point theorem
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