具有散度形式的拟线性椭圆型微分方程的区域振动准则

对一类具有散度形式的拟线性椭圆型微分方程建立了若干新的振动准则,所得结果仅依赖于方程在外区域Ω(?)R~n的一个区域序列的信息而有别于已知的大多数结论.     

On a singular case in the Hyers-Ulam-Rassias stability of the Wigner equation

Investigating the stability of the Wigner equation where the class of its approximate solutions is defined by the inequality

     

On the exceptional case of the characteristic singular equation with Cauchy kernel

We study the exceptional case of the characteristic singular integral equation with Cauchy kernel in which its coefficients admit zeros or singularities of complex orders at finitely many points of the contour. By reduction to a linear conjugation problem, we obtain an explicit solution formula and solvability conditions for this equation in weighted Hölder classes.     

Some results on a singular parabolic equation in one dimension case

This paper is concerned with the existence, nonexistence, uniqueness, and non‐uniqueness of solutions for a singular parabolic equation in one dimension case. For different cases of some constant m of the equation, we study the uniqueness of solutions for m > ? 1, the nonexistence of solutions for m ≤ ? p, and the existence and non‐uniqueness of solutions for ? p < m ≤ ? 1. The novelty of this paper lies in the study of nonexistence. Moreover, the other results of this paper extend some recent works. Copyright © 2013 John Wiley & Sons, Ltd.     

Regularity for the porous medium equation with variable exponent: The singular case

We extend to the singular case the results of [E. Henriques, J.M. Urbano, Intrinsic scaling for PDEs with an exponential nonlinearity, Indiana Univ. Math. J. 55 (5) (2006) 1701-1721] concerning the regularity of weak solutions of the porous medium equation with variable exponent. The method of intrinsic scaling is used to show that local weak solutions are locally continuous.     

Finite mean oscillation and the Beltrami equation

We prove the existence and uniqueness of homeomorphic ACL solutions to the Beltrami equation in the case when the dilatation coefficient of the equation has a majorant of finite mean oscillation.     

On the oscillation theory of the Sturm-Liouville problem with singular coefficients

The spectral Sturm-Liouville problem with distribution coefficients is examined. It is shown that the basic results concerning the number and the location of the zeros of eigenfunctions that are known in the smooth case remain valid in the general situation. The Chebyshev properties of systems of eigenfunctions are also investigated in the case where the weight function is positive.     

On the oscillation of a second-order delay equation

The oscillatory nature of two equations (r(t) y′(t))′ + p₁(t)y(t) = f(t), (r(t) y′(t))′ + p₂(t) y(t ? τ(t))= 0, is compared when positive functions p₁ and p₂ are not “too close” or “too far apart.” Then the main theorem states that if h(t) is eventually negative and a twice continuously differentiable function which satisfies (r(t) h′(t))′ + p₁(t) h(t) ? 0, then this inequality is necessary and sufficient for every bounded solution of (r(t) y′(t))′ + p₂(t) y(t ? τ(t)) = 0 to be nonoscillatory.