Abstract
By using the Krasnoselskii's fixed point theorem and operator spectral theorem, the existence of positive solutions for the nonlocal fourth-order boundary value problem with variable parameter , , , is considered, where is a parameter, and , .
Highlights
The existence of positive solutions for nonlinear fourth-order multipoint boundary value problems has been studied by many authors using nonlinear alternatives of Leray-Schauder, the fixed point theory, and the method of upper and lower solutions see, e.g., 1–15 and references therein
The multipoint boundary value problem is a special case of the boundary value problem with integral boundary conditions
Bai 16 studied the existence of positive solutions of nonlocal fourth-order boundary value problem u 4 t βu t λf t, u t, u t, 0 < t < 1, u0 u1 p s u s ds, 1.1
Summary
The existence of positive solutions for nonlinear fourth-order multipoint boundary value problems has been studied by many authors using nonlinear alternatives of Leray-Schauder, the fixed point theory, and the method of upper and lower solutions see, e.g., 1–15 and references therein. By using the Krasnoselskii’s fixed point theorem and operator spectral theorem, the existence of positive solutions for the nonlocal fourth-order boundary value problem with variable parameter u 4 tBtut λf t, u t , u t , 0 < t < 1, u 0 u 1
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