- Journal Article
Author: Nguyen Anh Dao (2018) - The purpose of this article is to establish the molecular decomposition of the homogeneous Besov-Morrey spaces associated with the Hermite operator H = −∆ + |x| 2 on the Euclidean space Rn. Particularly, we obtain some estimates for the operator H on the Hermite-Besov-Morrey spaces and the regularity results to the fractional Hermite equations (−∆ + |x| 2 ) su = f, and (−∆ + |x| 2 + I) su = f. Our results generalize some results by Anh and Thinh [1]
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- Journal Article
Author: Charles Castaing (2013) - Using the fiber product of Young measures and a new Green tyoe function we present a study of Bolza, relaxation and viscosity problem in Optimal Control Theory where the dynamic is governed by a second order ordinary differential equator (SODE) with m-point boudary conditions and control measures
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- Journal Article
Author: Le Xuan Truong (2011) - The article shows sufficient conditions for the existence of positive solutions to a multi-point boundary-value problem for a fourth-order differential equation. Our main tools are the Guo-Krasnoselskii fixed point theorem and the monotone iterative technique. We also show that the set of positive solutions is compact.
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- Journal Article
Author: Le Cong Nhan (2017) - By using Mawhin’s continuation theorem, we provide some sufficient conditions for the existence of solution for a class of high order differential equations of the form x^{(n)} =f(t,x,x^{\prime },\dots ,x^{(n-1)})\,, \quad t \in [0, 1]\,, associated with the integral boundary conditions at resonance. The interesting point is that we shall deal with the case of nontrivial kernel of arbitrary dimension corresponding to high order differential operator which will cause some difficulties in constructing the generalized inverse operator.
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- Journal Article
Author: Le Xuan Truong (2016) - In this work, we study an initial boundary value problem related to the nonlinear viscoelastic quation (1+a|u|q−2)ut−Δu+∫0tg(t−s)Δu(s)ds=b|u|p−2u. We show the exponential growth of solutions with Lp-norm for negative or positive initial energy.
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- Journal Article
Author: Le Cong Nhan (2017) - The main goal of this work is to study an initial–boundary value problem for a nonlinear pseudoparabolic equation with logarithmic nonlinearity. By using the potential well method and a logarithmic Sobolev inequality, we obtain results of existence or nonexistence of global weak solutions. In addition, we also provide sufficient conditions for the large time decay of global weak solutions and the finite time blow-up of weak solutions.
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- Journal Article
Author: Le Xuan Truong (2016) - The main goal of this paper is to study a model of the strongly nonlinear heat equation with viscoelastic term and nonlinear interior source of the form 1 + a|u; q−2 ut − ∆u + R t 0 g(t − s)∆u(s)ds = f(u), in Ω × [0, ∞), u = 0 on ∂Ω × [0, ∞), u(x, 0) = u0(x) in Ω.We show the results of local (or global) existence of weak solutions by using the Galerkin approximation method. In addition it has been provided sufficient conditions for the large time decay and the finite time blow-up of the weak solutions.
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- Journal Article
Author: Phan Dinh Phung (2013) - We consider a class of boundary value problem in a separable Banach space E, involving a nonlinear differential inclusion of fractional order with integral boundary conditions, of the form Dαu(t)∈F(t,u(t),Dα−1u(t)),a.e.,t∈[0,1],Iβu(t)|t=0=0,u(1)=∫01u(t)dt, (*) where Dα is the standard Riemann-Liouville fractional derivative, F is a closed valued mapping. Under suitable conditions we prove that the solutions set of (*) is nonempty and is a retract in WEα,1(I). An application in control theory is also provided by using the Young measures.
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- Journal Article
Author: Le Xuan Truong (2011) - The paper is devoted to the study a system of nonlinear wave equations associated with the mixed nonhomogeneous conditions. Existence of a weak solution is proved by using the Faedo–Galerkin method. Uniqueness, regularity and decay properties of solutions are also discussed.
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- Journal Article
Author: Charles Castating (2014) - Using a new Green type function we present a study of optimal control problem where the dynamic is governed by a second order ordinary differential equation (SODE) with m-point boundary condition.
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- Journal Article
Author: Le Xuan Truong (2013) - This paper is devoted to the study of the following nonlocal p-Laplacian functional
differential equation
−
φp(x
(t))
= λ f(t,x(t),x (t))
_x005F_x0004__x005F_x0005_ 1
0 f(s,x(s),x (s))ds_x005F_x0006_n , 0 < t < 1,
subject to multi point boundary conditions. We obtain some results on the existence of at least
one (when n ∈ Z+ ) or triple (when n = 0 ) pseudo-symmetric positive solutions by using fixedpoint
theory in cone.
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- Journal Article
Author: Nguyen Ngoc Trong (2018) - Let Delta L=−Delta+V be a Schrödinger operator on Rn,n≥3 , where V is a potential satisfying an appropriate reverse Hölder inequality. In this paper, we prove the boundedness of the Riesz transforms and the Littlewood–Paley square function associated with Schrödinger operators L in some new function spaces, such as new weighted Bounded Mean Oscillation (BMO) and weighted Lipschitz spaces, associated with L . Our results extend certain well-known results.
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- Journal Article
Author: Charles Castaing (2011) - We state various existence results of a class of a m-points boundary value problems including both second order differential ininclusion and evolusion; inclusion governed by a subdifferential operator involving the narrow conconvergence of Young measures and other tools. Some topological properties of solution sets are also discussed.
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- Journal Article
Author: Nguyen Ngoc Trong (2018) - Let \mathcal {L}=-{\Delta } + V be a Schrödinger operator on stratified Lie group G
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- Journal Article
Author: Do Huy Hoang (2017) - By using the Mawhin’s continuation theorem, we establish a sufficient condition for the existence of at least one solution of a boundary value problem for differential equation of fractional order. The new point is that we proved Fredholm property of the differential operator directly without going through the construction of projectors. Moreover, our work shows the way to construct the general continuous projector Q for both two cases of dimKerL∈{1,2}dimKerL∈{1,2}.
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- Journal Article
Author: Charles Castaing (2012) - We consider a class of m-point (m > 3) second order boundary value problem ( ) in a separable Banach space E of the formOpen image in new windowwhere F is a closed valued mapping. Under suitable compactness conditions on F we prove that the W2,1E([0,1]) -solutions of ( ) is compact and is a retract in C1E([0,1]) . A new existence result of W2,1E([0,1]) -solutions and a related relaxation problem are also provided, here F is no longer bounded.
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