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Scattering for the Radial Schrödinger Equation with Combined Power-type and Choquard-type Nonlinearities
In this paper, we show the scattering of the radial solution for the nonlinear Schrödinger equation with combined power-type and Choquard-type...
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Scattering for 3D Cubic Focusing NLS on the Domain Outside a Convex Obstacle Revisited
In this article, we consider the focusing cubic nonlinear Schrödinger equation(NLS) in the exterior domain outside of a convex obstacle in ℝ 3 with...
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Large time behaviour of a conservation law regularised by a Riesz-Feller operator: the sub-critical case
We study the large time behaviour of the solutions of a nonlocal regularisation of a scalar conservation law. This regularisation is given by a...
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BV Swee** Process Involving Prox-Regular Sets and a Composed Perturbation
In this paper we study the existence and properties of solutions for a discontinuous swee** process involving prox-regular sets in a Hilbert...
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Nonlinear Semigroups Built on Generating Families and their Lipschitz Sets
Under suitable conditions on a family ( I ( t )) t ≥ 0 of Lipschitz map**s on a complete metric space, we show that, up to a subsequence, the strong...
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On Well-posedness of Stochastic Anisotropic p-Laplace Equation Driven by Lévy Noise
Lions in Lions (
1969 ) solved the anisotropic p -Laplace equation in deterministic setting by considering the anisotropic p -Laplace operator in d -dimens... -
Approximate Controllability and Existence of Mild Solutions for Riemann-Liouville Fractional Stochastic Evolution Equations with Nonlocal Conditions of Order 1 < α < 2
In this paper, we consider the existence of mild solutions and approximate controllability for Riemann-Liouville fractional stochastic evolution...
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Existence of Solutions for Nonlinear Nonmonotone Evolution Equations in Banach Spaces with Anti-Periodic Boundary Conditions
The paper is devoted to the study of the existence of solutions for nonlinear nonmonotone evolution equations in Banach spaces involving...
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Existence of Solutions for Evolution Equations in Hilbert Spaces with Anti-Periodic Boundary Conditions and its Applications
We establish the existence of solutions for evolution equations in Hilbert spaces with anti-periodic boundary conditions. The energies associated to...
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AttRactivity for Fractional Evolution Equations with Almost Sectorial Operators
In this paper, we initiate the question of the attractivity of solutions for fractional evolution equations with almost sectorial operators. We...
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Variational and Quasi-Variational Inequalities with Gradient Type Constraints
This survey on stationary and evolutionary problems with gradient constraints is based on developments of monotonicity and compactness methods...
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Regularizing effects of homogeneous evolution equations: the case of homogeneity order zero
In this paper, we develop a functional analytical theory for establishing that mild solutions of first-order Cauchy problems involving homogeneous...
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Energy Scattering Theory for Electromagnetic NLS in Dimension Two
We study the well-posedness and long-time behavior of solution to both defocusing and focusing nonlinear Schr¨odinger equations with scaling critical...
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Scattering Theory for the Defocusing Fourth Order NLS with Potentials
Based on the endpoint Strichartz estimates for the fourth order Schrödinger equation with potentials for n ≥ 5 by [Feng, H., Soffer, A., Yao, X.:...
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Global well-posedness for the fifth-order mKdV equation
We prove the global well-posedness for the Cauchy problem of fifth-order modified Korteweg–de Vries equation in Sobolev spaces H s (ℝ) for s >
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Approximation Technique for Fractional Evolution Equations with Nonlocal Integral Conditions
We consider a class of fractional evolution equations with nonlocal integral conditions in Banach spaces. New existence of mild solutions to such a...