Homogeneous two-point problem for PDE of the second order in time variable and infinite order in spatial variables

Open Mathematics

Malanchuk Oksana¹  Nytrebych Zinoviy² 

[1] Danylo Halytsky Lviv National Medical University, Lviv, Ukraine;Lviv Polytechnic National University, Lviv, Ukraine;

关键词: null space;    pde;    two-point problem;    differential-symbol method;    35g15;   

DOI  :  10.1515/math-2017-0009

来源: DOAJ

【 摘 要 】

We prove that homogeneous problem for PDE of second order in time variable, and generally infinite order in spatial variables with local two-point conditions with respect to time variable, has only trivial solution in the case when the characteristic determinant of the problem is nonzero. In another, opposite case, we prove the existence of nontrivial solutions of the problem, and we propose a differential-symbol method of constructing them.

【 授权许可】

Unknown