Positive periodic solutions and nonlinear eigenvalue problems for functional differential equations

Positive periodic solutions and nonlinear eigenvalue problems for functional differential equations

This paper is devoted to investigate the existence of positive periodic solution for a functional differential equation in the form of λLx = −b(t) f (x(t − τ(t))), where Lx = x ′ (t) − a(t)g(x(t))x(t). By using well-known fixed point index theory in a cone, values of λ are determined for which there exist positive periodic solutions for the above functional differential equation. The dependence...

global results on some nonlinear partial differential equations for direct and inverse problems

در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...

Positive periodic solutions of functional differential equations

We consider the existence, multiplicity and nonexistence of positive o-periodic solutions for the periodic equation x0ðtÞ 1⁄4 aðtÞgðxÞxðtÞ lbðtÞf ðxðt tðtÞÞÞ; where a; bACðR; 1⁄20;NÞÞ are o-periodic, Ro 0 aðtÞ dt40; Ro 0 bðtÞ dt40; f ; gACð1⁄20;NÞ; 1⁄20;NÞÞ; and f ðuÞ40 for u40; gðxÞ is bounded, tðtÞ is a continuous o-periodic function. Define f0 1⁄4 limu-0þ f ðuÞ u ; fN 1⁄4 limu-N f ðuÞ u ; i0...

Positive Solutions for Nonlinear Differential Equations with Periodic Boundary Condition

Existence of Positive Periodic Solutions for Neutral Functional Differential Equations

We find sufficient conditions for the existence of positive periodic solutions of two kinds of neutral differential equations. Using Krasnoselskii’s fixed-point theorem in cones, we obtain results that extend and improve previous results. These results are useful mostly when applied to neutral equations with delay in bio-mathematics.