Existence of solutions for a class of nonlinear boundary value problems on half-line

Abstract

Consider the infinite interval nonlinear boundary value problemwhere u and v are principal and nonprincipal solutions of (p(t)x')' + q(t)x = 0, r 1 (t) = o (u(t)(v(t)) μ ) and r 2 (t) = o(v(t)(u(t)) μ ) for some μ (0, 1), and a and b are arbitrary but fixed real numbers. Sufficient conditions are given for the existence of a unique solution of the above problem for i = 1, 2. An example is given to illustrate one of the main results. Mathematics Subject Classication 2011: 34D05.

Boundary value problems on half‐line for second‐order nonlinear impulsive differential equations

“…Remark 2.1. Theorems above extend a recent study 14 to impulsive equations. For a related work concerning simpler type impulsive equations, see Akgöl and Zafer.…”

“…result in Equation 14. It is easy to see that any solution of the integral equation (14) is also a solution of (1).…”

“…Recently, a different approach that is based on asymptotic integration method involving principal and nonprincipal solutions 12 is introduced to study a certain class of BVPs on the half-line. 13,14 Motivated by the above results, we will study the existence of solutions of the impulsive BVP on half-line of the form…”

The Existence of Positive Solutions of Singular Initial-Value Problem for Second Order Differential Equations-2

“…In the mathematical literature there are many existence results on singular differential equations [3][4][5][6][7][8]. We are mainly motivated by [1] and the references therein.…”

Monotone iterative method for a class of nonlinear fractional differential equations on unbounded domains in Banach spaces

“…Boundary value problems of integer order on infinite intervals arise in the study of radially symmetric solutions of the nonlinear elliptic equations and have received considerable attention, for instance, see [32]- [40] and references therein. However, there are few papers dealing with nonlinear fractional differential equations on an unbounded domain [41]- [48].…”