In this article we apply an extension of an Avery type fixed point theorem to a family of boundary value problems for higher order ordinary differential equations. The theorem employs concave and convex functionals defined on a cone in a Banach space. We begin by extending a known application to a right focal boundary value problem for a second order problem to a conjugate boundary value problem for a second order problem. We then extend inductively to a two point boundary value problem for a higher order equation. Concavity of differentiable functions plays a key role in the application to second order equations. A concept of generalized concavity plays the same key role in the application to the higher order equation. (2010): 34B15, 34B27, 47H10.
Mathematics subject classification
This work explores Kink soliton solution, periodic soliton solution, and rational function solutions for the fractional generalized anti-cubic (FGAC) nonlinearity in fiber Bragg gratings (BGs). The rational fractional ((D_ζ^α G)/G)-expansion method is employed in conjunction with the idea of a conformable fractional derivative. Due to its nature, the soliton solution looks to have some restrictions.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.