Impulsive Integrodifferential Equations Involving Nonlocal Initial Conditions [PDF]
Advances in Difference Equations, 2011 We focus on a Cauchy problem for impulsive integrodifferential equations involving nonlocal initial conditions, where the linear part is a generator of a solution operator on a complex Banach space.
Wang Rong-Nian, Xia Jun
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On a Class of Multitime Evolution Equations with Nonlocal Initial Conditions [PDF]
Abstract and Applied Analysis, 2007 The existence and uniqueness of the strong solution for a multitime evolution equation with nonlocal initial conditions are proved. The proof is essentially based on a priori estimates and on the density of the range of the operator generated by the ...
F. Zouyed, F. Rebbani, N. Boussetila
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Existence results for impulsive systems with initial nonlocal conditions [PDF]
Mathematical Modelling and Analysis, 2013 We study the existence of solutions for nonlinear first order impulsive systems with nonlocal initial conditions. Our approach relies in the fixed point principles of Schauder and Perov, combined with a vector approach that uses matrices that converge to
Octavia Bolojan-Nica +2 more
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A note on the fractional Cauchy problems with nonlocal initial conditions [PDF]
Applied Mathematics Letters, 2011 The authors consider the Cauchy problem \[ D^\beta_t u(t)+ Au(t)= f(t,u(t))+ \int^t_0 K(t-s) g(s,u(s))\,ds,\quad t\in [0,T], \] with \(u(0)= H(u)\). Here \(D^\beta_t\) is a fractional time derivative of order \(\beta\in(0, 1)\), \(-A\) generates a compact analytic semigroup \(T(t)\) on a Banach space \(X\), \(u\in C([0,T]; X_\alpha)\) (\(X_\alpha\) the
Jin Liang +2 more
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First-order differential inclusions with nonlocal initial conditions [PDF]
Applied Mathematics Letters, 2002 It is considered the following nonlocal initial value problem \[ x'(t)\in F(t,x(t)),\quad t\in (0,1],\qquad x(0)+\sum_{k=1}^{m}a_{k}x(t_{k})=x_{0}, \tag{1} \] where \(F:(0,1]\times \mathbb{R}\to 2^{\mathbb{R}}\) is a set-valued map, \(x_{0}\in \mathbb{R}\) is given ...
Abdelkader Boucherif
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Semilinear integrodifferential equations with nonlocal initial conditions [PDF]
Computers and Mathematics With Applications, 2004 The paper is concerned with developing existence and uniqueness theorems for the Cauchy problem for semilinear integro-differential equations of convolution type. The sequence of theorems presented extends the existing results and can be applied, as is shown in the final section of the paper, to problems that arise in heat conduction in materials with ...
Jin Liang, Ti-Jun Xiao
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Controllability of semilinear boundary problems with nonlocal initial conditions [PDF]
Journal of Mathematical Analysis and Applications, 2006 The authors consider a semilinear nonautonomous boundary problem with nonlocal initial conditions. First, they prove the existence of a mild solution of the problem by constructing a contractive map; the solution is given by a variation of constants formula. Ideas of preceeding papers (in press and preprint) are used.
L Maniar
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Semilinear Volterra integrodifferential equations with nonlocal initial conditions [PDF]
Abstract and Applied Analysis, 1999 We establish the global existence of mild solutions to a class of nonlocal Cauchy problems associated with semilinear Volterra integrodifferential equations in a Banach space.
Mark Mckibben, Sergiu Aizicovici
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Controllability of time varying semilinear non-instantaneous impulsive systems with delay, and nonlocal conditions [PDF]
Archives of Control Sciences, 2022 In this paper we prove the exact controllability of a time varying semilinear system considering non-instantaneous impulses, delay, and nonlocal conditions occurring simultaneously.
Dalia Cabada +3 more
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Existence of Solutions to Fractional Mixed Integrodifferential Equations with Nonlocal Initial Condition [PDF]
Advances in Difference Equations, 2011 We study the existence and uniqueness theorem for the nonlinear fractional mixed Volterra-Fredholm integrodifferential equation with nonlocal initial condition , where , , and is a given function.
Karthikeyan P, Trujillo JJ, Anguraj A
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