Qualitative Theory on Oscillation of Solutions of Differential Equations

对偏泛函微分方程解振动的定性理论，即振动理论，得到了各种推广结果。建立了中立型抛物方程每一解振动的充分条件。此外，还得到了经典Rosenau-Burgers方程的一个推广的振动性定理，从而构造了向量抛物型和双曲型方程的振动性理论.离散型中立型双曲方程已被处理，但我们可以建立具有连续分布偏差变元的双曲方程的振动理论。关于这一主题的三篇论文已提交出版。其中两部是与中国东华大学陶友山教授的合作作品。一份关于肿瘤的合作论文被接受发表在《非线性》杂志上。此外，与东华大学严力坦教授的联合论文，讨论了双曲型双曲方程特征初值问题的振动性理论。我在斯洛伐克举行的国际会议（微分方程及其应用会议）上做了一次特邀演讲。然后，我可以讨论与雅罗斯瓦夫的数学家，我可以与Jaros教授（夸美纽斯大学）合作，建立Picone恒等式，并作出Sturmian比较定理的半线性椭圆方程的一阶项。我可以在富山大学举办“2003年富山微分方程会议”，并与特邀演讲人E.千叶大学的明切夫。

Various extended results were obtained for qualitative theory on oscillation of solutions of partial functional-differential equations, that is, oscillation theory. Sufficient conditions for every solution of parabolic equations of neutral type to be oscillatory were established. Moreover, oscillation theorems for a generalization of the classical Rosenau-Burgers equation were obtained^Oscillation theory for vector parabolic and hyperbolic equations could be constructed. Neutral hyperbolic equations of discrete type have been treated, but we could make oscillation theory for hyperbolic equations with continuous distributed deviating arguments. Three papers on this subject were submitted for publication. Two of them are joint works with Professor Youshan Tao of Dong Hua University in P.R.China. A paper on tumor which is a joint work was accpted for publication in the journal "Ndnlinearity". Furthermore, a joint paper with Professor Litan Yan of Dong Hua University which treat oscillation theory of characteristic initial value problems for hyperbolic equations of hyperbolic type was submitted for publication. I have given an invited lecture at the international conference(Conference on Differential Equations and Applications) held in Slovakia. Then I could discuss with Slovakian Mathematicians, and I could cooperate with Professor Jaros(Comenius University) to establish Picone identities and make Sturmian comparison theorems for half-linear elliptic equations with first order terms. I could hold "Toyama Conference on Differential Equations-2003" at Toyama University, and have fruitful discussions about Mathematics with the guest speaker, Professor E. Minchev of Chiba University.