Multiple Nonnegative Solutions for a Class of Fourth-Order BVPs Via a New Topological Approach

Open Access

Original research article

Author(s):

Salim Benslimane^a, Svetlin G. Georgiev^b, Karima Mebarki^c

^a Laboratory of Applied Mathematics, Faculty of Exact Sciences, Bejaia University, 06000 Bejaia, Algeria.
^b Department of Differential Equations, Faculty of Mathematics and Informatics, University of Sofia, Sofia, Bulgaria.
^c Laboratory of Applied Mathematics, Faculty of Exact Sciences, Bejaia University, 06000 Bejaia, Algeria.

Advances in the Theory of Nonlinear Analysis and its Applications 6(3), 390-404.

Received: August 2, 2021

Accepted: May 24, 2022

Published: May 26, 2022

Abstract

In this paper, we study a class of fourth-order boundary value problems with integral boundary conditions. The nonlinearity may have time-singularity and change sign. Moreover, it satisfies general polynomial growth conditions. A new topological approach is applied to prove the existence of at least two nonnegative classical solutions.
An example of application illustrates the existence result.

Keywords: ODE, fourth-order BVPs, nonnegative solution, fixed point, cone, sum of operators.

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APA Style

Benslimane, S., Georgiev, S., & Mebarki, K. (2022). Multiple nonnegative solutions for a class of fourth-order BVPs via a new topological approach. Advances in the Theory of Nonlinear Analysis and its Application, 6(3), 390-404.