NON ORDERED LOWER AND UPPER SOLUTIONS TO FOURTH ORDER PROBLEMS WITH FUNCTIONAL BOUNDARY CONDITIONS

作者：Cabada Alberto^*; Fialho Joao; Minhos Feliz

来源：Discrete and Continuous Dynamical Systems, 2011, 209-218.

• Higher order problems
• functional boundary value problems
• Nagumo condition
• lower and upper solutions

In this paper, given f : I x (C(I))(2) x R-2 -> R a L-1 - Caratheodory function, it is considered the functional fourth order equation
u((iv)) (x) = f (x, u, u', u ''(x), u '''(x))
together with the nonlinear functional boundary conditions
L-0 (u, u', u '', u(a)) = 0 = L-1 (u, u', u '', u' (a))
L-2 (u, u', u '', u '' (a), u ''' (a)) = 0 = L-3 (u, u', u '', u '' (b), u ''' (b)).
Here L-i, i = 0, 1, 2, 3, are continuous functions satisfying some adequate monotonicity assumptions.
It will be proved an existence and location result in presence of non ordered lower and upper solutions and without monotone assumptions on the right hand side of the equation.

• 出版日期2011-9