Lower and upper solutions for a fully nonlinear beam equation

Extremal solutions to fourth order discontinuous functional boundary value problems

“…Standard arguments (see for example ) give us the following a priori estimation on the first derivative of the solutions of problem . Lemma There exists , depending only on φ, γ and Γ, such that for every L 1 ‐Carathéodory function satisfying a Nagumo‐type condition in E, and every solution of such that we have that …”

“…Standard arguments (see for example [15]) give us the following a priori estimation on the first derivative of the solutions of problem (P v ).…”

On the Existence of Positive Solutions for a Fourth-Order Boundary Value Problem

“…where c is the positive eigenfunction of operator c related to its first eigenvalue ( ( c )) −1 , and 1 c ∈ 3 \ { } follows from (5).…”

“…In mechanics, BVP (1) is called cantilever beam equation. Owing to its importance in mechanics, the existence of solutions to this problem has been studied by many authors; see [1][2][3][4][5][6][7] and references therein.…”

Existence of solutions for a fully nonlinear fourth-order two-point boundary value problem

“…Most of the works in the above mentioned references allow only to have t, x or t, x, x in the right handside nonlinear function f , see [1, 2, 4-8, 10-12, 14-18, 20-24]. But the works on the fully nonlinear cases of which f contain explicitly t and every derivatives of x up to order three have been quite rarely seen, see [3,7,9,13,19].…”