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September  2014, 19(7): 2159-2168. doi: 10.3934/dcdsb.2014.19.2159

Inverse problems for singular differential-operator equations with higher order polar singularities

Mohammed Al Horani 1, and  Angelo Favini 2,

1. 

Department of Mathematics, The University of Jordan, Amman, Jordan
2. 

Dipartimento di Matematica, Università degli Studi di Bologna, Piazza di Porta S. Donato, 5, 40126 Bologna

Received  May 2013 Revised  April 2014 Published  August 2014

In this paper we study an inverse problem for strongly degenerate differential equations in Banach spaces. Projection method on suitable subspaces will be used to solve the given problem. A number of concrete applications to ordinary and partial differential equations is described.
Keywords: Banach space., Identification problem, first order equations, degenerate equation, inverse problem.
Mathematics Subject Classification: Primary: 34G10; Secondary: 34A5.
Citation: Mohammed Al Horani, Angelo Favini. Inverse problems for singular differential-operator equations with higher order polar singularities. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 2159-2168. doi: 10.3934/dcdsb.2014.19.2159
References:
[1]

M. Al Horani and A. Favini, Perturbation method for first and complete second order differential equations,, Preprint., ().   Google Scholar

[2]

M. Al Horani and A. Favini, An identification problem for first-order degenerate differential equations, Journal of Optimization Theory and Applications, 130 (2006), 41-60. doi: 10.1007/s10957-006-9083-y.  Google Scholar

[3]

R. Cross, A. Favini and Y. Yakubov, Perturbation results for multivalued linear operators, Progress in Nonlinear Differential Equations and Their Applications, 80 (2011), 111-130. doi: 10.1007/978-3-0348-0075-4_7.  Google Scholar

[4]

G. V. Demidenko and S. V. Uspenskii, Partial Differential Equations and Systems not Solvable With Respect to the Highest-Order Derivative, Marcel Dekker, Inc., New York, 2003. doi: 10.1201/9780203911433.  Google Scholar

[5]

A. Favaron and A. Favini, Fractional powers and interpolation theory for multivalued linear operators and applications to degenerate differential equations, Tsukuba J. Math., 35 (2011), 259-323.  Google Scholar

[6]

A. Faviniand and G. Marinoschi, Identification for degenerate problems of hyperbolic type, Applicable Analysis, 91 (2012), 1511-1527. doi: 10.1080/00036811.2011.630665.  Google Scholar

[7]

A. Favini and A. Yagi, Degenerate Differential Equations in Banach Spaces, Marcel Dekker. Inc. New York, 1999.  Google Scholar

[8]

F. Kappel and H. W. Knobloch, Gewöhnliche Differentialgleichungen, B. G. Teubner, Stuttgart, 1974.  Google Scholar

[9]

A. E. Taylor, Introduction to Functional Analysis, John Wiley & Sons, New York, 1958.  Google Scholar

[10]

H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amesterdam, 1978.  Google Scholar

[11]

L. A. Vlasenko, Evolutionary Models with Implicit and Degenerate Differential Equations, (rus.)- Dnepropetrovsk: System Technology, 2006. Google Scholar

[12]

K. Yosida, Functional Analysis, $6^{th}$ ed, Springer Verlag, Berlin-Heidelberg, New York, 1980.  Google Scholar

[13]

S. Yakubov and Y. Yakubov, Differential-operator Equations. Ordinary and Partial Differential Equations, Chapman & Hall, Boca Raton, USA, 2000.  Google Scholar

show all references

References:
[1]

M. Al Horani and A. Favini, Perturbation method for first and complete second order differential equations,, Preprint., ().   Google Scholar

[2]

M. Al Horani and A. Favini, An identification problem for first-order degenerate differential equations, Journal of Optimization Theory and Applications, 130 (2006), 41-60. doi: 10.1007/s10957-006-9083-y.  Google Scholar

[3]

R. Cross, A. Favini and Y. Yakubov, Perturbation results for multivalued linear operators, Progress in Nonlinear Differential Equations and Their Applications, 80 (2011), 111-130. doi: 10.1007/978-3-0348-0075-4_7.  Google Scholar

[4]

G. V. Demidenko and S. V. Uspenskii, Partial Differential Equations and Systems not Solvable With Respect to the Highest-Order Derivative, Marcel Dekker, Inc., New York, 2003. doi: 10.1201/9780203911433.  Google Scholar

[5]

A. Favaron and A. Favini, Fractional powers and interpolation theory for multivalued linear operators and applications to degenerate differential equations, Tsukuba J. Math., 35 (2011), 259-323.  Google Scholar

[6]

A. Faviniand and G. Marinoschi, Identification for degenerate problems of hyperbolic type, Applicable Analysis, 91 (2012), 1511-1527. doi: 10.1080/00036811.2011.630665.  Google Scholar

[7]

A. Favini and A. Yagi, Degenerate Differential Equations in Banach Spaces, Marcel Dekker. Inc. New York, 1999.  Google Scholar

[8]

F. Kappel and H. W. Knobloch, Gewöhnliche Differentialgleichungen, B. G. Teubner, Stuttgart, 1974.  Google Scholar

[9]

A. E. Taylor, Introduction to Functional Analysis, John Wiley & Sons, New York, 1958.  Google Scholar

[10]

H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, Amesterdam, 1978.  Google Scholar

[11]

L. A. Vlasenko, Evolutionary Models with Implicit and Degenerate Differential Equations, (rus.)- Dnepropetrovsk: System Technology, 2006. Google Scholar

[12]

K. Yosida, Functional Analysis, $6^{th}$ ed, Springer Verlag, Berlin-Heidelberg, New York, 1980.  Google Scholar

[13]

S. Yakubov and Y. Yakubov, Differential-operator Equations. Ordinary and Partial Differential Equations, Chapman & Hall, Boca Raton, USA, 2000.  Google Scholar

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