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Local solvability for a class of evolution equations
(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2010)
Motivated by the celebrated example of Y. Kannai of a linear partial differential operator which is hypoelliptic but not locally solvable, we consider it class of evolution operators with real-analytic coefficients and ...
Solving septics in radicals.
(2011-10-13)
A novel method to solve certain solvable septic equations is described. The method involves
conversion of the given septic to an octic equation by adding a root to it, and then decomposing the octic equation into two ...
Gevrey solvability near the characteristic set for a class of planar complex vector fields of infinite type
(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2009)
We study the Gevrey solvability of a class of complex vector fields, defined on Omega(epsilon) = (-epsilon, epsilon) x S(1), given by L = partial derivative/partial derivative t + (a(x) + ib(x))partial derivative/partial ...
Globally solvable systems of complex vector fields
(ACADEMIC PRESS INC ELSEVIER SCIENCESAN DIEGO, 2012)
We consider a class of involutive systems of n smooth vector fields on the n + 1 dimensional torus. We obtain a complete characterization for the global solvability of this class in terms of Liouville forms and of the ...
Equações diferenciais lineares sem solução
(Universidade Federal de Santa MariaBRMatemáticaUFSMPrograma de Pós-Graduação em Matemática, 2014-02-27)
In this work we present the proof of a result due to Lars Hörmander which establishes a necessary condition for a linear operator with variable coefficients is globally resolvable.
Comment on “Solution of Schrödinger equation for two different potentials using extended Nikiforov-Uvarov method and polynomial solutions of biconfluent Heun equation” [J. Math. Phys. 59, 053501 (2018)]
(American Institute of Physics, 2021-10)
We analyze some polynomial solutions to the Schrödinger equation with a central-field potential derived recently by means of the so-called extended Nikiforov-Uvarov method. We show that this approach does not produce the ...
Resolubilidade global de operadores lineares com coeficientes constantes
(Universidade Federal de Santa MariaBRMatemáticaUFSMPrograma de Pós-Graduação em Matemática, 2013-07-15)
In this dissertation we present a proof of a Bernard Malgrange theorem, which
establishes a necessary and sufficient condition for the global solvability of a linear
operator with constant coefficients.
Liouvillian solutions for second order linear diferential equations with polynomial coefcients
(Springer, 2020-09-10)
In this paper we present an algebraic study concerning the general second order
linear diferential equation with polynomial coefcients. By means of Kovacic’s
algorithm and asymptotic iteration method we fnd a degree ...
Solvability of nonlinear elliptic equations with gradient terms
(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2013)