In this paper, a periodic difference equation with saturable nonlinearity is considered. Using the linking theorem in combination with periodic approximations, we establish sufficient conditions on the nonexistence an...In this paper, a periodic difference equation with saturable nonlinearity is considered. Using the linking theorem in combination with periodic approximations, we establish sufficient conditions on the nonexistence and on the existence of homoclinic solutions. Our results not only solve an open problem proposed by Pankov, but also greatly improve some existing ones even for some special cases.展开更多
基金supported partially by the Specialized Fund for the Doctoral Program of Higher Eduction (Grant No.20071078001)Key Project of National Natural Science Foundation of China (Grant No. 11031002)+1 种基金Natural Science and Engineering Research Council of Canada (NSERC)Project of Scientific Research Innovation Academic Group for the Education System of Guangzhou City
文摘In this paper, a periodic difference equation with saturable nonlinearity is considered. Using the linking theorem in combination with periodic approximations, we establish sufficient conditions on the nonexistence and on the existence of homoclinic solutions. Our results not only solve an open problem proposed by Pankov, but also greatly improve some existing ones even for some special cases.
