Extremal solutions to fourth order discontinuous functional boundary value problems

Abstract

Key words Functional problems, extremal solutions, Greens functions, lower and upper solutions MSC (2010) 34B15, 34B10, 34K10In this paper, given f :is considered the functional fourth order equationtogether with the nonlinear functional boundary conditionsHere L i , i = 0, 1, 2, 3, satisfy some adequate monotonicity assumptions and are not necessarily continuous functions. It will be proved an existence and location result in presence of non ordered lower and upper solutions.

Existence and uniqueness of finite beam deflection on nonlinear non-uniform elastic foundation with arbitrary well-posed boundary condition

“…Throughout this paper, we assume that E, I, and l are fixed positive constants. From the classical Euler-Bernoulli beam theory [16], we have the following governing equation, which we denote by NDE(f , w), for the beam's vertical upward deflection u(x): (4)…”

“…Here, w(x) is a vertical downward load density on the beam, and -f (u(x), x) is the nonlinear and non-uniform elastic force density by the elastic foundation, which can depend on both the location x on the beam and the deflection u(x) at x. Beam deflection is one of the basic and important problems in structural mechanics and mechanical engineering, and it has a lot of applications [1,3,4,[7][8][9][10][11][12][13][15][16][17][18].…”

“…There have been various attempts [1,3,4,[7][8][9][10][11][12][13]17] to generalize the classical linear uniform problem LDE(w) to nonlinear or non-uniform settings. For infinitely long beam, Choi and Jang [7] obtained an existence and uniqueness result for the following infinite version: (4)…”

First Order Coupled Systems With Functional and Periodic Boundary Conditions: Existence Results and Application to an SIRS Model

“…Indeed, the functional part can deal with global boundary assumptions, such as minimum or maximum arguments, infinite multi-point data, and integral conditions on the several unknown functions. Functional problems, along with their features, can be seen in [14][15][16][17][18][19] and the references therein.…”

Existence results for functional first‐order coupled systems and applications

“…Indeed, the functional part can deal with global boundary assumptions, such as with minimum or maximum arguments, infinite multipoint data, integral conditions, … , on the several unknown functions. More details on functional problems can be seen in the previous studies [7][8][9][10][11][12] and the references therein.…”