Results 61 to 70 of about 722,802 (181)

Comparison principles for fractional differential equations with the Caputo derivatives

Advances in Difference Equations, 2018
In this paper, we deal with comparison principles for fractional differential equations involving the Caputo derivatives of order p with 0≤n ...
Ziqiang Lu, Yuanguo Zhu
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Verification theorem and construction of epsilon-optimal controls for control of abstract evolution equations [PDF]

We study several aspects of the dynamic programming approach to optimal control of abstract evolution equations, including a class of semilinear partial differential equations.
Fabbri, Giorgio, Gozzi, Fausto, Swiech, Andrzej   +2 more
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On the Bohr transform of almost-periodic solutions for some differential equations in abstract spaces

International Journal of Mathematics and Mathematical Sciences, 2001
We consider abstract differential equations of the form u′(t)=Au(t)+f(t) or u″(t)=Au(t)+f(t) in Banach spaces X, where f(⋅), ℝ→X is almost-periodic, while A is a linear operator, 𝒟(A)⊂X→X.
Samuel Zaidman
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Existence and continuous dependence of mild solutions for fractional abstract differential equations with infinite delay

Electronic Journal of Qualitative Theory of Differential Equations, 2012
In this paper, we prove the existence, uniqueness, and continuous dependence of the mild solutions for a class of fractional abstract differential equations with infinite delay.
Haiping Ye, Jiao Liu, Jianming Gao
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Existence of solutions to a second order partial differential equation with nonlocal conditions

Electronic Journal of Differential Equations, 2003
Using the cosine function theory, we prove the existence of mild and classical solutions for an abstract second-order Cauchy problem with nonlocal conditions.
Eduardo Hernandez M.
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Abstract methods in differential equations

, 2003
The author surveys his research of the last twenty years on a functional analytic approach to quasilinear parabolic systems. The main topics are: local well-posedness and global existence, linearization and stability criteria, coercivity conditions for parabolic systems, interpolation-extrapolation scales and quasilinear problems.
openaire   +3 more sources

Infinitesimal symmetry transformations of matrix-valued differential equations: An algebraic approach

, 2018
The study of symmetries of partial differential equations (PDEs) has been traditionally treated as a geometrical problem. Although geometrical methods have been proven effective with regard to finding infinitesimal symmetry transformations, they present ...
Papachristou, C. J.
core  

On generalized Wazewski and Lozinskii inequalities for semilinear abstract differential-delay equations

Journal of Inequalities and Applications, 1998
A semilinear abstract differential-delay equation with a nonautonomous linear part is considered. Solution estimates are derived. They generalize Wazewski and Lozinskii inequalities. Conditions for global stability are established.
Gil' MI
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Well-posedness of semilinear stochastic wave equations with H\"{o}lder continuous coefficients

, 2016
We prove that semilinear stochastic abstract wave equations, including wave and plate equations, are well-posed in the strong sense with an $\alpha$-H\"{o}lder continuous drift coefficient, if $\alpha \in (2/3,1)$.
Masiero, Federica, Priola, Enrico
core  

Existence results for a class of semi-linear evolution equations

Electronic Journal of Differential Equations, 2001
We prove the existence of regular solutions for the quasi-linear evolution $$ {d over dt}(x(t)+g(t,x(t))=Ax(t)+f(t,x(t)), $$ where $A$ is the infinitesimal generator of an analytic semigroup of bounded linear operators defined on a Banach space and the ...
Eduardo Hernandez M.
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