On the Solvability of Fourth-Order Two-Point Boundary Value Problems

Ravi P. Agarwal and Petio S. Kelevedjiev
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Ravi P. Agarwal: Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363-8202, USA
Petio S. Kelevedjiev: Department of Mathematics, Technical University of Sliven, 8800 Sliven, Bulgaria

Mathematics, 2020, vol. 8, issue 4, 1-19

Abstract: In this paper, we study the solvability of various two-point boundary value problems for x ( 4 ) = f ( t , x , x ′ , x ″ , x ? ) , t ∈ ( 0 , 1 ) , where f may be defined and continuous on a suitable bounded subset of its domain. Imposing barrier strips type conditions, we give results guaranteeing not only positive solutions, but also monotonic ones and such with suitable curvature.

Keywords: fourth-order differential equation; two-point boundary value problems; existence; positive or non-negative, monotone, convex or concave solutions; sign conditions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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