scholarly journals An abstract nonlocal functional-differential second order evolution Cauchy problem

2018 ◽  
Vol 4 ◽  
Keyword(s):  
Cauchy Problem ◽  
Second Order ◽  
Nonlocal Functional ◽  
Functional Differential

scholarly journals Nonlinear conservation laws for the Schrödinger boundary value problems of second order

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ming Ren ◽  
Shiwei Yun ◽  
Zhenping Li
Keyword(s):  
Cauchy Problem ◽  
Conservation Laws ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Maximum Modulus ◽  
Second Order ◽  
Nonlinear Conservation Laws ◽  
The Cauchy Problem ◽  
Modulus Method ◽  
Semilinear Schrödinger Equation

AbstractIn this paper, we apply a reliable combination of maximum modulus method with respect to the Schrödinger operator and Phragmén–Lindelöf method to investigate nonlinear conservation laws for the Schrödinger boundary value problems of second order. As an application, we prove the global existence to the solution for the Cauchy problem of the semilinear Schrödinger equation. The results reveal that this method is effective and simple.

The weighted Cauchy problem for linear functional differential equations with strong singularities

2011 ◽  
Vol 18 (3) ◽  
pp. 577-586
Author(s):  
Zaza Sokhadze
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Linear Functional ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Initial Point ◽  
Higher Order ◽  
Well Posedness ◽  
Deviating Arguments ◽  
Functional Differential

Abstract The sufficient conditions of well-posedness of the weighted Cauchy problem for higher order linear functional differential equations with deviating arguments, whose coefficients have nonintegrable singularities at the initial point, are found.

scholarly journals On the Existence of Positive Periodic Solutions for Second-Order Functional Differential Equations with Multiple Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Qiang Li ◽  
Yongxiang Li
Keyword(s):  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Index Theory ◽  
Second Order ◽  
Multiple Delays ◽  
First Eigenvalue ◽  
Fixed Point Index Theory ◽  
Existence Conditions ◽  
Functional Differential ◽  
Periodic Boundary Problem

The existence results of positiveω-periodic solutions are obtained for the second-order functional differential equation with multiple delaysu″(t)+a(t)u(t)=f(t,u(t),u(t−τ1(t)),…,u(t−τn(t))), wherea(t)∈C(ℝ)is a positiveω-periodic function,f:ℝ×[0,+∞)n+1→[0,+∞)is a continuous function which isω-periodic int, andτ1(t),…,τn(t)∈C(ℝ,[0,+∞))areω-periodic functions. The existence conditions concern the first eigenvalue of the associated linear periodic boundary problem. Our discussion is based on the fixed-point index theory in cones.

scholarly journals Integrated cosine functions

1996 ◽  
Vol 19 (3) ◽  
pp. 575-580 ◽  
Author(s):  
Quan Zheng
Keyword(s):  
Banach Space ◽  
Cauchy Problem ◽  
Second Order ◽  
Basic Theory ◽  
Cosine Function ◽  
Integrated Semigroups ◽  
Approximation Theorems ◽  
The Relationship ◽  
Cosine Functions

In order to the second order Cauchy problem(CP2):x″(t)=Ax(t),x(0)=x∈D(An),x″(0)=y∈D(Am)on a Banach space, Arendt and Kellermann recently introduced the integrated cosine function. This paper is concerned with its basic theory, which contain some properties, perturbation and approximation theorems, the relationship to analytic integrated semigroups, interpolation and extrapolation theorems.

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