Results 81 to 90 of about 19,755 (210)

Existence of mild solutions for nonlocal perturbed evolution equations with infinite state-dependent delay in Fréchet spaces [PDF]

Archives of Control Sciences
In this work, we give sufficient conditions to get the existence of mild solutions for two classes of first-order semilinear functional and neutral functional perturbed evolution equations with infinite state-dependent delay when the conditions are ...
Selma Baghli-Bendimerad, Imane Abibssi
doaj   +1 more source

Regularisation effects of nonlinear semigroups

, 2016
One introduces natural and simple methods to deduce $L^{s}$-$L^{\infty}$-re\-gularisation estimates for $1\le s< \infty$ of nonlinear semigroups holding uniformly for all time with sharp exponents from natural Gagliardo-Nirenberg inequalities. From $L^{q}$-$L^{r}$ Gagliardo-Nirenberg inequalities, $1\le q, r\le \infty$, one deduces $L^{q}$-$L^{r ...
Coulhon, Thierry, Hauer, Daniel
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A class of one-parameter nonlinear semigroups with differentiable approximating semigroups [PDF]

Proceedings of the American Mathematical Society, 1977
Suppose that T is a strongly continuous semigroup of transformations on a subset C of a Banach space X. For δ > 0 \delta > 0 , consider U δ ( t ) = { ( δ −
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Optimal Control Strategies and Continuous Dependence for Stochastic Hilfer Fractional Systems With Delay: A Volterra‐Fredholm Integro‐Differential Approach

Optimal Control Applications and Methods, Volume 46, Issue 6, Page 2708-2726, November/December 2025.
The graphical abstract highlights our research on Sobolev Hilfer fractional Volterra‐Fredholm integro‐differential (SHFVFI) control problems for 1<ϱ<2$$ 1<\varrho <2 $$. We begin with the Hilfer fractional derivative (HFD) of order (1,2) in Sobolev type, which leads to Volterra‐Fredholm integro‐differential equations.
Marimuthu Mohan Raja, V. Vijayakumar, Chun‐Wei Tsai, Kalyana Chakravarthy Veluvolu   +3 more
wiley   +1 more source

Exponential Attractor for Lattice System of Nonlinear Boussinesq Equation

Discrete Dynamics in Nature and Society, 2013
We study the lattice dynamical system of a nonlinear Boussinesq equation. We first verify the Lipschitz continuity of the continuous semigroup associated with the system.
Min Zhao, Shengfan Zhou
doaj   +1 more source

Nonlinear holomorphic semigroups [PDF]

Pacific Journal of Mathematics, 1975
Hayden, T. L., Massey, F. J.
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Mild solutions for perturbed evolution equations with infinite state-dependent delay

Electronic Journal of Qualitative Theory of Differential Equations, 2013
In this paper, we give sufficient conditions to get the existence of mild solutions for two classes of first order partial and neutral of perturbed evolution equations by using the nonlinear alternative of Avramescu for contractions operators in Fréchet ...
Djillali Aoued, Selma BAGHLI-BENDIMERAD
doaj   +1 more source

Existence of solutions for nonlinear impulsive neutral integro-differential equations of Sobolev type with nonlocal conditions in Banach spaces

Electronic Journal of Differential Equations, 2013
In this article, we prove the existence of mild and strong solutions for nonlinear impulsive integro-differential equations of Sobolev type with nonlocal initial conditions.
Bheeman Radhakrishnan, Aruchamy Mohanraj, Velu Vinoba   +2 more
doaj  

Nonlinear perturbations of analytic semigroups

Semigroup Forum, 1991
From the author's text: ``This is a survey article which outlines recent work on relatively continuous perturbations of analytic semigroups in Banach spaces. The results are described from the point of view of nonlinear semigroup theory. Necessary and sufficient conditions are discussed for a semilinear operator \(A+B\) to be the full infinitesimal ...
openaire   +2 more sources

Existence results for nondensely defined semilinear functional differential inclusions in Fréchet spaces

Electronic Journal of Qualitative Theory of Differential Equations, 2005
In this paper, a recent Frigon nonlinear alternative for contractive multivalued maps in Fréchet spaces, combined with semigroup theory, is used to investigate the existence of integral solutions for first order semilinear functional differential ...
Johnny Henderson, Abdelghani Ouahab
doaj   +1 more source