In this paper we study the problem of the existence of homoclinic solutions to a Schrodinger equation of the form x''-V(t)x+x(3)=0, where V is a stepwise potential. The technique of proof is based on a topological method, relying on the properties of the transformation of continuous planar paths (the S.A.P. method), together with the application of the classical Conley-Wazewski method.
Multiple homoclinic solutions for a one-dimensional Schrödinger equation / Dambrosio, Walter; Papini, Duccio. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S. - ISSN 1937-1632. - 9:4(2016), pp. 1025-1038. [10.3934/dcdss.2016040]
Multiple homoclinic solutions for a one-dimensional Schrödinger equation
PAPINI, Duccio
2016
Abstract
In this paper we study the problem of the existence of homoclinic solutions to a Schrodinger equation of the form x''-V(t)x+x(3)=0, where V is a stepwise potential. The technique of proof is based on a topological method, relying on the properties of the transformation of continuous planar paths (the S.A.P. method), together with the application of the classical Conley-Wazewski method.
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