On multiple positive solutions of positone and non-positone problems.
We prove a theorem on the existence of solutions of a first order functional differential inclusion governed by a class of nonconvex sweeping process with a noncompact perturbation.
New sufficient conditions of the existence and uniqueness of the solution of a boundary problem for an ordinary differential equation of -th order with certain functional boundary conditions are constructed by the method of a priori estimates.
In this paper we study nonlinear second order differential equations subject to separated linear boundary conditions and to linear impulse conditions. Sign properties of an associated Green’s function are investigated and existence results for positive solutions of the nonlinear boundary value problem with impulse are established. Upper and lower bounds for positive solutions are also given.
The differential equation of the form , a ∈ (0,∞), is considered and solutions u with u(0) = 0 and (u(t))² + (u’(t))² > 0 on (0,∞) are studied. Theorems about existence, uniqueness, boundedness and dependence of solutions on a parameter are given.
We consider a Lidstone boundary value problem in at resonance. We prove the existence of a solution under the assumption that the nonlinear part is a Carathéodory map and conditions similar to those of Landesman-Lazer are satisfied.