Scattering properties of eigenparameter-dependent impulsive Sturm-Liouville equations. (English) Zbl 1437.34085
Summary: The main aim of this work is to investigate the properties of scattering solutions and the scattering function of an impulsive Sturm-Liouville boundary value problem (ISBVP). It is important that the boundary condition depend on the eigenvalue parameter. After getting the Jost solution of this ISBVP, we find the scattering function and resolvent operator. Also, we discuss the discrete spectrum of this boundary value problem in detail. Finally, we present examples on an unperturbated ISBVPs to demonstrate the application of our results.
MSC:
| 34L25 | Scattering theory, inverse scattering involving ordinary differential operators |
| 34B24 | Sturm-Liouville theory |
| 34A37 | Ordinary differential equations with impulses |
| 34L05 | General spectral theory of ordinary differential operators |
Keywords:
scattering solution; resolvent operator; impulsive condition; spectral parameter; eigenvalue; boundary value problemReferences:
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