Khalil Ezzinbi

Existence of solutions for neutral functional differential evolution equations with nonlocal conditions

Abstract In this paper, by using fractional power of operators and Sadovskiis fixed point theorem, we study the existence of mild and strong solutions of semilinear neutral functional differential evolution equations with nonlocal conditions. The results we obtained are a generalization and continuation of the recent results on this issue. In the end, an example is given to show the application of our results.

Existence and regularity of solutions for some neutral partial differential equations with nonlocal conditions

Abstract In this work, we establish several results about the existence and regularity of solutions for some neutral partial differential equations with nonlocal conditions. We assume that the linear part generates a strongly continuous semigroup on a general Banach space.

Local existence and stability for some partial functional differential equations with infinite delay

Generally, this disclosure provides systems, methods and computer readable media for a protected memory view in a virtual machine (VM) environment enabling nested page table access by trusted guest software outside of VMX root mode. The system may include an editor module configured to provide access to a nested page table structure, by operating system (OS) kernel components and by user space applications within a guest of the VM, wherein the nested page table structure is associated with one of the protected memory views. The system may also include a page handling processor configured to secure that access by maintaining security information in the nested page table structure.

Strict solutions of nonlinear hyperbolic neutral differential equations

Abstract In this work, we study a class of abstract semilinear functional differential equations of a neutral type. Our main results concern the existence, uniqueness, and regularity of solutions. We assume that the linear part is nondensely defined, closed, and satisfies the Hille-Yosida condition.

C n -almost automorphic solutions for partial neutral functional differential equations

In this work, we study the existence of C n -almost periodic solutions and C n -almost automorphic solutions (nu2009≥u20091), for partial neutral functional differential equations. We prove that the existence of a bounded integral solution on ℝ+ implies the existence of C n -almost periodic and C n -almost automorphic strict solutions. When the exponential dichotomy holds for the homogeneous linear equation, we show the uniqueness of C n -almost periodic and C n -almost automorphic strict solutions.

Existence of solutions for a class of partial neutral differential equations

Abstract In this work, we obtain the local and the global existence for a class of partial neutral differential equations with a non dense domain. We assume that the nonlinear part is continuous and the linear part satisfy a compactness property.

Periodic solutions for some partial functional differentialequations

We study the existence of a periodic solution for some partial n functional differential equations. We assume nthat the linear part is nondensely defined and satisfies the nHille-Yosida condition. In the nonhomogeneous linear case, we nprove the existence of a periodic solution under the existence of na bounded solution. In the nonlinear case, using a fixed-point ntheorem concerning set-valued maps, we establish the existence of na periodic solution.

Pseudo almost automorphic solutions for some partial functional differential equations with infinite delay

In this work, we study the existence of pseudo almost automorphic solution for some partial functional differential equations with infinite delay. We assume that the undelayed part is not necessarily densely defined and satisfies the Hille–Yosida condition. We use the variation of constant formula developed recently in 1 to get the existence and uniqueness of pseudo almost automorphic solution when the linear equation has an exponential dichotomy. We also give an application of the abstract results to a Lotka–Volterra model with diffusion.

Partial Functional Differential Equations: Reduction of Complexity and Applications

The aim of this work is to reduce the complexity of partial functional differential equations. We suppose that the undelayed part is not necessarily densely defined and satisfies the Hille-Yosida condition. The delayed part is continuous. We prove the dynamic of solutions are obtained through an ordinary differential equations that is well-posed in a finite dimensional space. The powerty of this results is used to show the existence of almost automorphic solutions for partial functional differential equations. For illustration, we provide an application to the Lotka-Volterra model with diffusion and delay.