CoInvestigator(Kenkyūbuntansha) 
YASHIRO Yoshimatsu Osaka Electrocommunication University Faculty of Engineering, assistant profess, 工学部, 助教授 (10140229)
YAMAHARA Hideo Osaka Electrocommunication University Faculty of Engineering, assistant profess, 工学部, 助教授 (30103344)
MIZOHATA Sigeru Osaka Electrocommunication University Faculty of Engineering, professor, 工学部, 教授 (20025216)

Budget Amount *help 
¥1,300,000 (Direct Cost : ¥1,300,000)
Fiscal Year 1992 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1991 : ¥800,000 (Direct Cost : ¥800,000)

Research Abstract 
Sakata gave [1] a sufficient condition for a Lienard system x^^・=yF(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_<n1>, 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 CauchyKovalevskaya theorem holds for systems of partial differential equations.
