Abstract
We consider the fourth-order two-point boundary value problem , , , where is a parameter, is given constant, with on any subinterval of , satisfies for all , and , , for some . By using disconjugate operator theory and bifurcation techniques, we establish existence and multiplicity results of nodal solutions for the above problem.
Highlights
The deformations of an elastic beam in equilibrium state with fixed both endpoints can be described by the fourth-order ordinary differential equation boundary value problem u λh t f u, 0 < t < 1, 1.1 u 0 u 1 u 0 u 1 0, where f : R → R is continuous, λ ∈ R is a parameter
In 1984, Agarwal and chow 1 firstly investigated the existence of the solutions of the problem 1.1 by contraction mapping and iterative methods, subsequently, Ma and Wu 2 and Yao 3, 4 studied the existence of positive solutions of this problem by the Krasnosel’skii fixed point theorem on cones and Leray-Schauder fixed point theorem
Boundary Value Problems h t ≡ 0, Korman 5 investigated the uniqueness of positive solutions of the problem 1.1 by techniques of bifurcation theory
Summary
The deformations of an elastic beam in equilibrium state with fixed both endpoints can be described by the fourth-order ordinary differential equation boundary value problem u λh t f u , 0 < t < 1, 1.1 u 0 u 1 u 0 u 1 0, where f : R → R is continuous, λ ∈ R is a parameter. Boundary Value Problems h t ≡ 0, Korman 5 investigated the uniqueness of positive solutions of the problem 1.1 by techniques of bifurcation theory. The existence of sign-changing solution for this problem have not been discussed.
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