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Solutions of weakly nonlinear systems bounded on R in resonance

Alexander A. Boichuk

National Academy of Sciences of Ukraine
Institute of Mathematics
Tereshchenkivs'ka str.3
252601, Kyiv 4
Ukraine



Abstract


Conditions for the existence of solutions bounded on R are obtained for a weakly nonlinear ordinary differential system in assumption that the operator L defined by linear homogeneous system is a Fredholm operator and the corresponding inhomogeneous linear system has an r-parametric set of solutions bounded on R. If L is a Fredholm operator with index zero and in case r = 1 we obtain the well-known result of K. Palmer.


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Contact information


Alexander A. Boichuk

National Academy of Sciences of Ukraine
Institute of Mathematics
Tereshchenkivs'ka str.3
252601, Kyiv 4
Ukraine

e-mail: boichuk@imath.kiev.ua



3rd ENOC ProceedingsIndex