Results 11 to 20 of about 39 (28)
Well-posedness for the fourth-order Schrödinger equations with quadratic nonlinearity
Advances in Differential Equations, 2011 This paper is concerned with 1-D quadratic semilinear fourth-order Schrödinger equations. Motivated by the quadratic Schrödinger equations in the pioneer work of Kenig-Ponce-Vega [12], three bilinearities uv, uv, uv for functions u, v : R× [0, T ] 7→ C ...
Jiqiang Zheng
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HYBRID DELAY EVOLUTION SYSTEMS WITH NONLINEAR CONSTRAINTS
Dynamic systems and applications, 2018 Motivated by the importance of reaction-diffusion systems in modeling real processes with memory, we are interested in the existence of mild solutions for systems of abstract delay evolution equations subjected to general nonlinear constraints.
Octavia-Maria Bolojan, Radu Precup
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Convergence of functionals and its applications to parabolic equations
Abstract and Applied Analysis, Volume 2004, Issue 11, Page 907-933, 2004., 2004 Asymptotic behavior of solutions of some parabolic equation associated with the p‐Laplacian as p → +∞ is studied for the periodic problem as well as the initial‐boundary value problem by pointing out the variational structure of the p‐Laplacian, that is, ∂φp(u) = −Δpu, where φp : L2(Ω) → [0, +∞]. To this end, the notion of Mosco convergence is employed
Goro Akagi
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Bounded solutions of nonlinear Cauchy problems
Abstract and Applied Analysis, Volume 7, Issue 12, Page 637-661, 2002., 2002 For a given closed and translation invariant subspace Y of the bounded and uniformly continuous functions, we will give criteria for the existence of solutions u ∈ Y to the equation u′(t) + A(u(t)) + ωu(t)∍f(t), t ∈ ℝ, or of solutions u asymptotically close to Y for the inhomogeneous differential equation u′(t) + A(u(t)) + ωu(t)∍f(t), t > 0, u(0) = u0,
Josef Kreulich
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Advances in Nonlinear Analysis, 2016 We present sufficient conditions on the existence of solutions, with various specific almost periodicity properties, in the context of nonlinear, generally multivalued, non-autonomous initial value differential equations,
Kreulich Josef
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International Journal of Applied Mechanics and Engineering, 2015 A fourth order nonlinear evolution equation, which is a good starting point for the study of nonlinear water waves as first pointed out by Dysthe (1979) is derived for gravity waves propagating at the interface of two superposed fluids of infinite depth ...
D.P. Majumder, A.K. Dhar
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On nonlinear evolution equation of second order in Banach spaces
Open Mathematics, 2018 Here we study the existence of a solution and also the behavior of the existing solution of the abstract nonlinear differential equation of second order that, in particular, is the nonlinear hyperbolic equation with nonlinear main parts, and in the ...
Soltanov Kamal N.
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, 2012 In this paper, nonlocal Cauchy problems for fractional evolution equations involving Volterra-Fredholm type integral operators are investigated. Some new existence theorems of mild solutions are presented by using fractional calculus, Hölder inequality ...
Jinrong Wang, Wei Wei, Michal Feckan
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A Determining Form for a Nonlocal System
Advanced Nonlinear Studies, 2017 This work is concerned with constructing a finite dimensional form (named determining form) by adding a feedback control term through an interpolation operator. The dynamics of the determining form is consistent with those of the original system.
Bai Lu, Yang Meihua
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Transformation of p-gradient flows to p′-gradient flows in metric spaces
Analysis and Geometry in Metric SpacesWe explicitly construct parameter transformations between gradient flows in metric spaces, called curves of maximal slope, having different exponents when the associated function and the associated metric space satisfy a suitable convexity condition ...
Shimoyama Sho
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