Higher order functional boundary value problems without monotone assumptions

Abstract

In this paper, given f :

Lower and upper solutions method for a problem of an elastic beam whose one end is simply supported and the other end is sliding clamped

“…Hence, the inequality (24) is true. however, the current result is different from that of [11]. In fact, for problem (5), if we let…”

“…Obviously, this is different from our Definition 3. [ 11,Theorem 5] requires that the second derivatives of lower solution γ and upper solution σ are well ordered, i.e. γ ′′ (x) ≤ σ ′′ (x)…”

“…However, the second derivatives of the lower and upper solutions must be ordered. Fialho et al [11] proved the existence and location result in the presence of not necessarily ordered lower and upper solutions for the higher order functional boundary value problem (here we only state the special case with n = 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.…”