| Co-Investigator(Kenkyū-buntansha) |
YASHIRO Yoshimatsu Osaka Electro-communication University Faculty of Engineering, assistant profess, 工学部, 助教授 (10140229)
YAMAHARA Hideo Osaka Electro-communication University Faculty of Engineering, assistant profess, 工学部, 助教授 (30103344)
MIZOHATA Sigeru Osaka Electro-communication University Faculty of Engineering, professor, 工学部, 教授 (20025216)
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| Research Abstract |
Sakata gave [1] a sufficient condition for a Lienard system x^^・=y-F(x),y^^・=-g(x) to possess several periodic solutions, where xg(x)>0 for x*0, F(-x)=-F(x) and F(x) is oscillatory as x is increasing. In particular, even if the amplitude of F(x) is monotonically decreasing, the system possesses several periodic solutions, whenever | F(x) | is small. In the case that g(x)=lambdax for some positive lambda, it seems that we can give a sufficient condition for the system to possess periodic solutions which is concerned with value of *_<l_n>F(x)dx, where l_n =[x_<n-1>, x_n] and {x_n} is a sequence of positive zeros of F(x). But this is an open problem.
Mizohata investigated singular boundary value problem for heat operator u/(x,y,t) =DELTAu(x,y,t) in OMEGA={(x,y)ly*0}, a(x)u/+b(x)u=0 for y=0, u(x,y,0)=u_0(x,y), where a(x)^2+b(x)^2=1 and order of zeros of a(x) is finite. He showed that if the problem is uniquely solvable and if a(x)*0, then b(x)=1 for zeros of a(x).
Yamahara, with Matsumoto, showed that Cauchy-Kovalevskaya theorem holds for systems of partial differential equations.
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