Homoclinic solutions in periodic difference equations with saturable nonlinearity |
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| Authors: | ZHOU Zhan YU JianShe & CHEN YuMing School of Mathematics Information Science Guangzhou University Guangzhou China |
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| Institution: | ZHOU Zhan1,YU JianShe1 & CHEN YuMing2 1School of Mathematics and Information Science,Guangzhou University,Guangzhou 510006,China,2Department of Mathematics,Wilfrid Laurier University,Waterloo N 2L 3C 5,Canada |
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| Abstract: | 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. |
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| Keywords: | homoclinic solution periodic difference equation linking theorem periodic approximation |
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