scholarly journals Existence and uniqueness theorem on mild solutions to the Keller–Segel system in the scaling invariant space

2012 ◽  
Vol 252 (2) ◽  
pp. 1213-1228 ◽  
Author(s):  
Hideo Kozono ◽  
Yoshie Sugiyama ◽  
Takuya Wachi
Keyword(s):  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Mild Solutions ◽  
Existence And Uniqueness Theorem ◽  
Invariant Space ◽  
Scaling Invariant

scholarly journals Existence and Uniqueness of Pseudo Almost Automorphic Mild Solutions to Some Classes of Partial Hyperbolic Evolution Equations

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
Zhanrong Hu ◽  
Zhen Jin
Keyword(s):  
Evolution Equation ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Existence And Uniqueness Theorem ◽  
Abstract Result ◽  
Almost Automorphic ◽  
Pseudo Almost Automorphic

We will establish an existence and uniqueness theorem of pseudo almost automorphic mild solutions to the following partial hyperbolic evolution equation(d/dt)[u(t)+f(t,Bu(t))]=Au(t)+g(t,Cu(t)),  t∈ℝ,under some assumptions. To illustrate our abstract result, a concrete example is given.

scholarly journals A UNIFIED EXISTENCE AND UNIQUENESS THEOREM FOR STOCHASTIC EVOLUTION EQUATIONS

2009 ◽  
Vol 81 (1) ◽  
pp. 33-46
Author(s):  
A. JENTZEN ◽  
P. E. KLOEDEN
Keyword(s):  
Diffusion Coefficient ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Trace Class ◽  
Existence And Uniqueness Theorem ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Class Noise

AbstractAn existence and uniqueness theorem for mild solutions of stochastic evolution equations is presented and proved. The diffusion coefficient is handled in a unified way which allows a unified theorem to be formulated for different cases, in particular, of multiplicative space–time white noise and trace-class noise.

scholarly journals Fuzzy Conformable Fractional Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Atimad Harir ◽  
Said Melliani ◽  
Lalla Saadia Chadli
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Uniqueness Theorem ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Existence And Uniqueness Theorem ◽  
Fractional Differential ◽  
Fractional Differentiability ◽  
Derivatives Of ◽  
Fuzzy Fractional Differential Equation

In this study, fuzzy conformable fractional differential equations are investigated. We study conformable fractional differentiability, and we define fractional integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy fractional differential equation by using the concept of conformable differentiability. This concept is based on the enlargement of the class of differentiable fuzzy mappings; for this, we consider the lateral Hukuhara derivatives of order q ∈ 0,1 .

scholarly journals A Picard Theorem for iterative differential equations

2009 ◽  
Vol 42 (2) ◽  
Author(s):  
Wen-rong Li ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equations ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Existence And Uniqueness Theorem ◽  
Picard Theorem ◽  
Iterative Differential Equations

AbstractA Picard type existence and uniqueness theorem is established for iterative differential equations of the form

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