Abstract
In the present paper, we investigate the existence of solutions to second order nonlinear boundary value problems (BVPs) involving the distributional Henstock-Kurzweil integral. The present results in this article are generalizations of previous results in the literature.
Highlights
1 Introduction New existence results are derived for solutions of the second order differential equation
The existence of solutions of boundary value problems have been studied by many authors [ – ]
The boundary conditions model the behavior of a thermostat where the sensor measures the temperature
Summary
New existence results are derived for solutions of the second order differential equation. Subject to the boundary conditions x ( ) = , βx ( ) + x(η) = , where x , x stand for the distributional derivative of the function x ∈ C[ , ], C[ , ] denotes the space where the functions x : [ , ] → R are continuous, f is a distribution (generalized function), β is a positive constant and η ∈ [ , ]. The existence of solutions of boundary value problems have been studied by many authors [ – ]. Chew and Flordeliza, in [ ], generalized the classical Carathéodory’s existence theorem on the Cauchy problem x = f (t, x) with x( ) =. Liang et al Boundary Value Problems (2015) 2015:73 distributional derivatives to discuss In Section , we apply Schauder’s fixed point theorem to verify the existence of BVP In Section , we give an example to illustrate Theorem . in this paper
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
