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

Abstract

In this paper, we study the solvability of various two-point boundary value problems for, 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.

On the Solvability of Nonlinear Third-Order Two-Point Boundary Value Problems

“…Here, we demonstrate this on problem (1), (4) but it can be done for the rest of the BVPs considered in this paper. Similar results for various other two-point boundary conditions can be found in R. Agarwal and P. Kelevedjiev [16] and P. Kelevedjiev and T. Todorov [15].…”

“…It is a variant of Reference [12] (Chapter I, Theorem 5.1 and Chapter V, Theorem 1.2). Its proof can be found in Reference [15]; see also the similar result in Reference [16] (Theorem 4). 8) and (7) 1 , (8) are equivalent.…”

Existence for Two-Point nth Order Boundary Value Problems under Barrier Strips

“…This property provides a priori bounds for the (n − 1)th derivatives of the solutions to (1) λ , ( 2) and (1) λ , (3), see Lemma 2. Various other applications of barrier strips can be found for example in R. Agarwal et al [11][12][13].…”

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

“…For instance, the deformation of an elastic beam under an external force h supported at both ends is described by the linear boundary value problem x (4) (t) = h(t), t ∈ (0, 1), x(0) = x(1) = x ′′ (0) = x ′′ (1) = 0, where vanishing moments at the ends of the attached beam motivate the boundary conditions (see [9] for more details). The existence of solutions for nonlinear fourth-order BVPs has gained much interest in the last years (see, e.g., [2,3,4,6,10,11,12,13,15,17]). Boundary value problems with integral boundary conditions constitute a very interesting and important class of problems.…”