On a nonlinear elliptic boundary value problem
The periodic boundary value problem u''(t) = f(t,u(t),u'(t)) with u(0) = u(2π) and u'(0) = u'(2π) is studied using the generalized method of upper and lower solutions, where f is a Carathéodory function satisfying a Nagumo condition. The existence of solutions is obtained under suitable conditions on f. The results improve and generalize the work of M.-X. Wang et al. [5].
New sufficient conditions for the existence of a solution of the boundary value problem for an ordinary differential equation of -th order with certain functional boundary conditions are constructed by a method of a priori estimates.
An inverse problem for a nonlocal problem describing the temperature of a conducting device is studied.
This paper presents sufficient conditions for the existence of solutions to boundary-value problems of second order multi-valued differential inclusions. The existence of extremal solutions is also obtained under certain monotonicity conditions.
We prove the existence of extremal solutions of Dirichlet boundary value problems for u''a + fa(t,u,u'a) = 0 in l∞(A) between a generalized pair of upper and lower functions with respect to the coordinatewise ordering, and for f quasimonotone increasing in its second variable.