Existence and non-existence of maximal solutions for y" = f(x, y, y') *
We consider the boundary value problem involving the one dimensional -Laplacian, and establish the precise intervals of the parameter for the existence and non-existence of solutions with prescribed numbers of zeros. Our argument is based on the shooting method together with the qualitative theory for half-linear differential equations.
We study the existence and positivity of solutions of a highly nonlinear periodic differential equation. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ a modification of Krasnoselskii’s fixed point theorem introduced by T. A. Burton ([4], Theorem 3) to show the existence and positivity of solutions of the equation.
The system of nonlinear differential equations is under consideration, where and are positive constants and and are positive continuous functions on . There are three types of different asymptotic behavior at infinity of positive solutions of (). The aim of this paper is to establish criteria for the existence of solutions of these three types by means of fixed point techniques. Special emphasis is placed on those solutions with both components decreasing to zero as , which can be...
The paper deals with the existence and uniqueness of 2π-periodic solutions for the odd-order ordinary differential equation , where is continuous and 2π-periodic with respect to t. Some new conditions on the nonlinearity to guarantee the existence and uniqueness are presented. These conditions extend and improve the ones presented by Cong [Appl. Math. Lett. 17 (2004), 727-732].
The paper presents an existence result for global solutions to the finite dimensional differential inclusion being defined on a closed set A priori bounds for such solutions are provided.