Abstract
The existence results of multiple monotone and convex positive solutions for some fourth-order multi-point boundary value problems are established. The nonlinearities in the problems studied depend on all order derivatives. The analysis relies on a fixed point theorem in a cone. The explicit expressions and properties of associated Green's functions are also given.
Highlights
Boundary value problems for second and higher order nonlinear differential equations play a very important role in both theory and applications
The deformations of an elastic beam in the equilibrium state can be described as a boundary value problem of some fourth-order differential equations
Owing to its importance in application, the existence of positive solutions for nonlinear second and higher order boundary value problems has been studied by many authors
Summary
Boundary value problems for second and higher order nonlinear differential equations play a very important role in both theory and applications. Owing to its importance in application, the existence of positive solutions for nonlinear second and higher order boundary value problems has been studied by many authors. When it comes to positive solutions for nonlinear fourth-order ordinary differential equations, two point boundary value problems are studied extensively, see [16,17,18,19,20,21,22,23,24].
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