Abstract
In this paper, we consider a class of nonlinear third-order boundary value problems with integral boundary conditions on time scales. By applying a generalization of the Leggett-Williams fixed point theorem, we establish the existence of at least three positive solutions. The discussed problem involves both an increasing and positive homomorphism, which generalizes the p-Laplacian operator. As an application, we give an example to illustrate our results.
Highlights
1 Introduction In recent years, much attention has been paid to boundary value problems with integral boundary conditions due to their various applications in chemical engineering, thermoelasticity, population dynamics, heat conduction, chemical engineering underground water flow, thermo-elasticity, and plasma physics
The study of dynamic equations on time scales, which has been created in order to unify the study of differential and difference equations, is an area of mathematics that has recently received a lot of attention; many results on this issue have been well documented in the monographs [ – ]
To the best of our knowledge, there is no paper published on the existence of multiple positive solutions to nonlinear third-order boundary value problems with integral boundary conditions on time scales
Summary
Much attention has been paid to boundary value problems with integral boundary conditions due to their various applications in chemical engineering, thermoelasticity, population dynamics, heat conduction, chemical engineering underground water flow, thermo-elasticity, and plasma physics.
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