Existence and Nonexistence Results for a Fourth-Order Boundary Value Problem with Sign-Changing Green’s Function

Nikolay D. Dimitrov () and Jagan Mohan Jonnalagadda
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Nikolay D. Dimitrov: Department of Mathematics, University of Ruse, 7017 Ruse, Bulgaria
Jagan Mohan Jonnalagadda: Department of Mathematics, Birla Institute of Technology and Science Pilani, Hyderabad 500078, India

Mathematics, 2024, vol. 12, issue 16, 1-12

Abstract: In this paper, we consider a fourth-order three-point boundary value problem. Despite the fact that the corresponding Green’s function changes its sign on the square of its definition, we obtain the existence of at least one positive and decreasing solution under some suitable conditions. The results are based on the classical Krasosel’skii’s fixed point theorem in cones. Then, we impose some sufficient conditions that allow us to deduce nonexistence results. In the end, some examples are given in order to illustrate our main results.

Keywords: fourth-order equation; positive solutions; sign-changing Green’s function; fixed point theorems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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