American Institute of Mathematical Sciences

Advanced
February & March  2007, 18(2&3): 405-428. doi: 10.3934/dcds.2007.18.405

On the inverse Sturm-Liouville problem

Russell Johnson 1, and  Luca Zampogni 2,

1. 

Dipartimento di Sistemi e Informatica, Università di Firenze, 50139 Firenze
2. 

Dipartimento di Matematica U. Dini, Università di Firenze, Italy

Received  April 2006 Revised  July 2006 Published  March 2007

We pose and solve an inverse problem of an algebro-geometric type for the classical Sturm-Liouville operator. We use techniques of nonautonomous dynamical systems together with methods of classical algebraic geometry.
Keywords: nonautonomous differential equations., algebraic curves, Sturm-Liouville operator.
Mathematics Subject Classification: 34A55, 37B55, 37K1.
Citation: Russell Johnson, Luca Zampogni. On the inverse Sturm-Liouville problem. Discrete & Continuous Dynamical Systems - A, 2007, 18 (2&3) : 405-428. doi: 10.3934/dcds.2007.18.405
[1]

Chuan-Fu Yang, Natalia Pavlovna Bondarenko. A partial inverse problem for the Sturm-Liouville operator on the lasso-graph. Inverse Problems & Imaging, 2019, 13 (1) : 69-79. doi: 10.3934/ipi.2019004
[2]

N. A. Chernyavskaya, L. A. Shuster. Spaces admissible for the Sturm-Liouville equation. Communications on Pure & Applied Analysis, 2018, 17 (3) : 1023-1052. doi: 10.3934/cpaa.2018050
[3]

Elimhan N. Mahmudov. Optimal control of Sturm-Liouville type evolution differential inclusions with endpoint constraints. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-18. doi: 10.3934/jimo.2019066
[4]

Elimhan N. Mahmudov. Optimization of fourth order Sturm-Liouville type differential inclusions with initial point constraints. Journal of Industrial & Management Optimization, 2020, 16 (1) : 169-187. doi: 10.3934/jimo.2018145
[5]

Peter Howard, Alim Sukhtayev. The Maslov and Morse indices for Sturm-Liouville systems on the half-line. Discrete & Continuous Dynamical Systems - A, 2020, 40 (2) : 983-1012. doi: 10.3934/dcds.2020068
[6]

Guglielmo Feltrin. Multiple positive solutions of a sturm-liouville boundary value problem with conflicting nonlinearities. Communications on Pure & Applied Analysis, 2017, 16 (3) : 1083-1102. doi: 10.3934/cpaa.2017052
[7]

Jędrzej Śniatycki. Integral curves of derivations on locally semi-algebraic differential spaces. Conference Publications, 2003, 2003 (Special) : 827-833. doi: 10.3934/proc.2003.2003.827
[8]

Vu Hoang Linh, Volker Mehrmann. Spectral analysis for linear differential-algebraic equations. Conference Publications, 2011, 2011 (Special) : 991-1000. doi: 10.3934/proc.2011.2011.991
[9]

Yingjie Bi, Siyu Liu, Yong Li. Periodic solutions of differential-algebraic equations. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 0-0. doi: 10.3934/dcdsb.2019232
[10]

Arno Berger. Counting uniformly attracting solutions of nonautonomous differential equations. Discrete & Continuous Dynamical Systems - S, 2008, 1 (1) : 15-25. doi: 10.3934/dcdss.2008.1.15
[11]

Lars Grüne, Peter E. Kloeden, Stefan Siegmund, Fabian R. Wirth. Lyapunov's second method for nonautonomous differential equations. Discrete & Continuous Dynamical Systems - A, 2007, 18 (2&3) : 375-403. doi: 10.3934/dcds.2007.18.375
[12]

Bernd Aulbach, Martin Rasmussen, Stefan Siegmund. Invariant manifolds as pullback attractors of nonautonomous differential equations. Discrete & Continuous Dynamical Systems - A, 2006, 15 (2) : 579-596. doi: 10.3934/dcds.2006.15.579
[13]

Shouchuan Hu, Nikolaos S. Papageorgiou. Nonlinear Neumann equations driven by a nonhomogeneous differential operator. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1055-1078. doi: 10.3934/cpaa.2011.10.1055
[14]

Jason R. Scott, Stephen Campbell. Auxiliary signal design for failure detection in differential-algebraic equations. Numerical Algebra, Control & Optimization, 2014, 4 (2) : 151-179. doi: 10.3934/naco.2014.4.151
[15]

Seyedeh Marzieh Ghavidel, Wolfgang M. Ruess. Flow invariance for nonautonomous nonlinear partial differential delay equations. Communications on Pure & Applied Analysis, 2012, 11 (6) : 2351-2369. doi: 10.3934/cpaa.2012.11.2351
[16]

Yuan Guo, Xiaofei Gao, Desheng Li. Structure of the set of bounded solutions for a class of nonautonomous second order differential equations. Communications on Pure & Applied Analysis, 2010, 9 (6) : 1607-1616. doi: 10.3934/cpaa.2010.9.1607
[17]

Ismael Maroto, Carmen NÚÑez, Rafael Obaya. Dynamical properties of nonautonomous functional differential equations with state-dependent delay. Discrete & Continuous Dynamical Systems - A, 2017, 37 (7) : 3939-3961. doi: 10.3934/dcds.2017167
[18]

Luca Bisconti, Marco Spadini. On the set of harmonic solutions of a class of perturbed coupled and nonautonomous differential equations on manifolds. Communications on Pure & Applied Analysis, 2017, 16 (4) : 1471-1492. doi: 10.3934/cpaa.2017070
[19]

Yongxin Jiang, Can Zhang, Zhaosheng Feng. A Perron-type theorem for nonautonomous differential equations with different growth rates. Discrete & Continuous Dynamical Systems - S, 2017, 10 (5) : 995-1008. doi: 10.3934/dcdss.2017052
[20]

Ismael Maroto, Carmen Núñez, Rafael Obaya. Exponential stability for nonautonomous functional differential equations with state-dependent delay. Discrete & Continuous Dynamical Systems - B, 2017, 22 (8) : 3167-3197. doi: 10.3934/dcdsb.2017169

2018 Impact Factor: 1.143

Tools

Metrics

  • PDF downloads (14)
  • HTML views (0)
  • Cited by (5)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences