Let be an integer part of and be the number of positive divisor of . Inspired by some results of M. Jutila (1987), we prove that for , where is the Euler constant and is the Piatetski-Shapiro sequence. This gives an improvement upon the classical result of this problem.
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.
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 -dimensional domains (). 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...
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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