Nonresonant singular fourth-order boundary value problems

Abstract

Existence results are presented for the nonresonant singular fourth-order boundary value problemwhere f : [0, 1] × (0, ∞) → (0, ∞) is continuous and β < π 2 . Existence is established via the fixed point theorem in cones.

A numerical scheme for multi-point special boundary-value problems and application to fluid flow through porous layers

“…A lot of research has been conducted where many numerical schemes have been developed for solving boundary-value problems [1][2][3][4][5][6][7][8][9][10][11]. Many of these schemes are based on discretization of the space and finite difference approximations of the derivatives.…”

Existence and uniqueness theorems for fourth-order singular boundary value problems

“…Problems of the form (1.1), for example, are used to model such phenomena as the deflection of an elastic beam supported at the endpoints. Most of the available literature on fourth-order boundary value problems, for instance [1][2][3][4][5], showed that the equations had at least single and multiple positive solutions. Recently, Lin [6] considered the following fourth-order boundary value problem:…”

Non-trivial solutions for nonlinear fourth-order elastic beam equations

“…It is worth noticing that an assumption of type (1.1) is completely novel for fourth-order differential problems, while an assumption of type (1.2), when it is used, usually needs additional conditions on the nonlinear term. Here, no asymptotic condition at infinity on g is required, and the existence of non-trivial solutions is also obtained for problems where the results in the literature, such as those in [1,10,12,13], cannot be applied (see Remark 4.4). This paper is arranged as follows.…”

“…The existence of at least one non-zero solution for nonlinear fourth-order differential problems has been investigated in several works by using different approaches such as fixed point theorems, lower and upper solutions methods, critical point theory and so on (see, for example, [1,10,12,13]). In these cited papers, under suitable assumptions on the nonlinear term, several types of existence results have been obtained.…”

“…Existence results of at least one solution, or multiple solutions, or even infinitely many solutions have been established by many authors using fixed point theorems, lower and upper solutions methods, and critical point theory (see, for example, [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and the references therein). The aim of this paper is to establish the existence of at least one non-trivial solution under suitable non-standard growth conditions on the nonlinearity in an appropriate interval without any asymptotic conditions at infinity.…”