Local analytic solutions of a functional differential equation with a deviating argument depending on the state derivative near resonance

Local Analytic Solutions of an Iterative Functional Differential Equation Depend on the State Derivative

Analytic Solutions of a First Order Functional Differential Equation with a State Derivative Dependent Delay

This article concerns the first-order functional differential equation x′(z) = x(p(z) + bx′(z)) with the distinctive feature that the argument of the unknown function depends on the state derivative. An existence theorem is established for analytic solutions and systematic methods for deriving explicit solutions are also given.

Analytic Solutions of an Iterative Functional Differential Equation with Delays Depending On State

This This paper is concerned with an iterative functional differential equation with the form C z z x b az x z x     ,)) ((1) (.By constructing a convergent power series solution of an auxiliary equation C z z g z ag z g z ag z g z g z g a b        ), ()] () ()][ () ([)] () ([ 2 2 2      the analytic solutions for the original equation are obtained. We not only discuss the cons...

Lazer-Leach Type Conditions on Periodic Solutions of Liénard Equation with a Deviating Argument at Resonance

and Applied Analysis 3 (3) The Brouwer degree deg{JQN,Ω∩Ker L, 0} ̸ = 0, where J : ImQ → Ker L is an isomorphism. Then equation Lx = Nx has at least one solution onD(L)∩Ω. 3. Main Results In this section, we will use the continuation theorem introduced in Section 2 to prove the existence of periodic solutions of (1). To this end, we first quote some notations and definitions. Let X and Y be two ...

Fourth-Order Differential Equation with Deviating Argument

and Applied Analysis 3 Motivated by 14, 15 , here we study the existence of AL-solutions for 1.1 . The approach is completely different from the one used in 15 , in which an iteration process, jointly with a comparison with the linear equation y 4 q t y 2 0, is employed. Our tools are based on a topological method, certain integral inequalities, and some auxiliary functions. In particular, for ...