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Frequent oscillation in a nonlinear partial difference equation

Jun Yang;  Yu Zhang;  Sui Cheng — 2007

Open Mathematics

This paper is concerned with a class of nonlinear delay partial difference equations with variable coefficients, which may change sign. By making use of frequency measures, some new oscillatory criteria are established. This is the first time oscillation of these partial difference equations is discussed by employing frequency measures.

Asymptotic lower bounds for eigenvalues of the Steklov eigenvalue problem with variable coefficients

Yu Zhang;  Hai Bi;  Yidu Yang — 2021

Applications of Mathematics

In this paper, using a new correction to the Crouzeix-Raviart finite element eigenvalue approximations, we obtain asymptotic lower bounds of eigenvalues for the Steklov eigenvalue problem with variable coefficients on d -dimensional domains ( d = 2 , 3 ). In addition, we prove that the corrected eigenvalues converge to the exact ones from below. The new result removes the conditions of eigenfunction being singular and eigenvalue being large enough, which are usually required in the existing arguments about...

Well-posedness of a class of non-homogeneous boundary value problems of the Korteweg-de Vries equation on a finite domain

Eugene Kramer;  Ivonne Rivas;  Bing-Yu Zhang — 2013

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we study a class of Initial-Boundary Value Problems proposed by Colin and Ghidaglia for the Korteweg-de Vries equation posed on a bounded domain (0). We show that this class of Initial-Boundary Value Problems is locally well-posed in the classical Sobolev space (0) for > -3/4, which provides a positive answer to one of the open questions of Colin and Ghidaglia [6 (2001) 1463–1492].

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