Results 141 to 150 of about 53,002 (179)

Abstract reaction–diffusion systems with nonlocal initial conditions

Nonlinear Analysis: Theory, Methods & Applications, 2014
The authors study the abstract nonlinear first-order delay reaction-diffusion system with nonlocal initial conditions \[ \begin{aligned} & u'(t) \in Au(t)+f(t,u_{t},v_{t}), \;t\in [ 0,\infty),\\ & v'(t) \in Bv(t)+g(t,u_{t},v_{t}), \;t\in [ 0,\infty),\\ & u(t)=p(u,v)(t), \;t\in [ -\tau ,0],\\ & v(t)=q(u,v)(t), \;t\in [ -\tau ,0],\end{aligned}\tag{1 ...
Burlică, Monica-Dana, Roşu, Daniela, Vrabie, Ioan I.   +2 more
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Nonlocal initial conditions for fractional diffusion problems

AIP Conference Proceedings, 2017
We discuss the existence and uniqueness of solutions of nonlinear space-fractional diffusion equations subject to an initial condition of integral type. Our approach shall rely on fixed point theorems.We discuss the existence and uniqueness of solutions of nonlinear space-fractional diffusion equations subject to an initial condition of integral type ...
Abdelkader Boucherif, Boumediene Abdellaoui, Tarik Mohamed Touaoula   +2 more
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On Impulsive Hyperbolic Differential Inclusions with Nonlocal Initial Conditions

Journal of Optimization Theory and Applications, 2008
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Chang, Y.-K., Nieto, J. J., Li, W.-S.
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Regularity for evolution equations with nonlocal initial conditions

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2017
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Chen, Pengyu, Zhang, Xuping, Li, Yongxiang   +2 more
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Arbitrary initial conditions of nonlocal hidden variables

Physical Review D, 1984
A deterministic nonlocal hidden-variable theory with arbitrary initial conditions is consistent with quantum theory. The sufficiency conditions for the hidden variables are developed.
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Viability for delay evolution equations with nonlocal initial conditions

Nonlinear Analysis: Theory, Methods & Applications, 2015
The authors consider the problem \[ u'(t)\in Au(t)+f(t,u_t),\,\, t\in R_+, \] \[ u(t)=g(u)(t), \,\, t\in [-\sigma, 0], \] where \(X\) is a real Banach space; \(A : D(A) \subset X \rightsquigarrow X\) is the infinitesimal generator of a nonlinear semigroup; \(K : R_+ \rightsquigarrow \overline{D(A)};\) \(L = \{(t, \phi) \in R_+ \times C_\sigma \,\, :\,\,
Necula, Mihai, Popescu, Marius, Vrabie, Ioan I.   +2 more
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Study on Integrodifferential Evolution Systems with Nonlocal Initial Conditions

2021
The work is concerned with systems of abstract integrodifferential equations with general nonlocal initial conditions. To allow the nonlinear terms of the equations to behave as independently as possible, we employ a vector approach based on matrices, vector-valued norms, and a vector version of Krasnoselskii's fixed point theorem for a sum of two ...
Sylvain Koumla, Radu Precup
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A nonlinear fractional partial integro‐differential equation with nonlocal initial value conditions

Mathematical Methods in the Applied Sciences, 2023
In this work, we study a new nonlinear partial integro‐differential equation with nonlocal initial value conditions and investigate the solutions of this equation. By considering an equivalent implicit integral equation via series, we prove the uniqueness of solutions of the equation by Babenko's approach, Banach's contraction principle, and the ...
Chenkuan Li, Reza Saadati, Donal O'Regan, Radko Mesiar, Andrii Hrytsenko   +4 more
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Existence of Semilinear Differential Equations with Nonlocal Initial Conditions

Acta Mathematica Sinica, English Series, 2006
The author considers the existence of mild solutions for semilinear Cauchy problems \[ u'(t) =Au(t) +f(t,u(t)), \quad t\in [0,b]\text{ a.e., }u(0) =g(u) +u_0, \] where \(A\) is an infinitesimal generator of a strongly continuous semigroup \(T(t)\) of bounded linear operators in a Banach space \(X\), \(f: [0,b] \times X\to X\), \(g\in C([0,b] ;X)\) are ...
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Existence results for systems with coupled nonlocal initial conditions

Nonlinear Analysis: Theory, Methods & Applications, 2014
In this interesting paper the authors discuss the system of the first order differential equations \[ u_j'=f_j(t,u_1,\dots,u_n), \, j=1, 2,\dots,n, \] a.e. on the interval \([0,1]\) associated with the conditions of the form \[ u_j(0)=\sum_{i=1}^n\alpha_{ji}[u_i], \] where the symbol \(\alpha_{ji}[u_i]\) stands for the known Riemann-Stieltjes integral \
Bolojan Nica O, INFANTE, GENNARO, Precup R.   +2 more
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