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Generalized Morrey spaces associated to Schrödinger operators and applications

Nguyen Ngoc TrongLe Xuan Truong — 2018

Czechoslovak Mathematical Journal

We first introduce new weighted Morrey spaces related to certain non-negative potentials satisfying the reverse Hölder inequality. Then we establish the weighted strong-type and weak-type estimates for the Riesz transforms and fractional integrals associated to Schrödinger operators. As an application, we prove the Calderón-Zygmund estimates for solutions to Schrödinger equation on these new spaces. Our results cover a number of known results.

Existence results for a class of high order differential equation associated with integral boundary conditions at resonance

Le Cong NhanDo Huy HoangLe Xuan Truong — 2017

Archivum Mathematicum

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 ' , , x ( n - 1 ) ) , t [ 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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