# On a representation of the solution of the inverse Sturm-Liouville problem on the entire line

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The article presents a mathematical study which describes a solution of the inverse Sturm-Liouville problem on a real axis. The study uses the classical approach of several authors to solve the problem including L. D. Faddeev, B. M. Levitan, and V. A. Marchenko and considers the Jost functions...

- Solvability of Sturm-Liouville boundary value problems with impulses. Zhang, Li; Huang, Xiankai; Xing, Chunfeng // Boundary Value Problems;Dec2013, Vol. 2013 Issue 1, p1
In this paper, we consider a kind of Sturm-Liouville boundary value problems with impulsive effects. By using the mountain pass theorem and Ekelandâ€™s variational principle, the existence of two positive solutions and two negative solutions is established. Moreover, we do not assume that...

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The representation of the norming constants by 2 spectra was studied by Levitan, Gasymov (and others) for the Sturm-Liouville problem with boundary conditions y(0) cos Î± + y"(0) sin Î± = 0, y(Ï€) cos Î² + y'(Ï€) sin Î² = 0, when sin Î± â‰ 0 and sin Î² â‰ 0. We...

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In this work we study a question on stability and instability of the basis property of a system of eigenfunctions of a Sturm-Liouville operator with an integral perturbation of one of boundary conditions.

- Principal Functions of Non-Selfadjoint Sturm-Liouville Problems with Eigenvalue-Dependent Boundary Conditions. Yokuş, Nihal // Abstract & Applied Analysis;2011, Special section p1
We consider the operator L generated in LÂ² (â„+) by the differential expression l(y) = -y" + q(x)y, x âˆˆ â„+ := (0,âˆž) and the boundary condition y' (0)/y(0) = Î±0 + Î±1Î» + Î±2Î»Â², where q is a complexvalued function and Î±i âˆˆ â€¦, i = 0, 1,2 with...

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The article presents a mathematical research which discusses the generalizations of Levinson's theorem for the reconstruction of the Sturm-Liouville problem with general boundary conditions. Details include the definition of the problem, the vectors and coefficients in the boundary conditions,...

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Deals with a study which presented results of positive and monotone solutions of a complete Sturm-Liouville boundary value problem. Background to the study; Results; Theorems and proofs.

- NECESSARY AND SUFFICIENT CONDITION FOR THE BOUNDEDNESS OF THE GERBER-SHIU FUNCTION IN DEPENDENT SPARRE ANDERSEN MODEL. ORBÁN-MIHÁLYKÓ, ÉVA; MIHÁLYKÓ, CSABA // Miskolc Mathematical Notes;2014, Vol. 15 Issue 1, p159
In this paper we investigate the boundedness of the Gerber-Shiu expected discounted penalty function applied in insurance mathematics. We give a necessary and sufficient condition for its boundedness. This condition is essentially the boundedness of the conditional expectation given the ruin...

- AN APPLICATION OF A GLOBAL BIFURCATION THEOREM TO THE EXISTENCE OF SOLUTIONS FOR INTEGRAL INCLUSIONS. DOMACHOWSKI, STANISŁAW // Electronic Journal of Differential Equations;2008, Vol. 2008, Special section p1
We prove the existence of solutions to Hammerstein integral inclusions of weakly completely continuous type. As a consequence we obtain an existence theorem for differential inclusions, with Sturm-Liouville boundary conditions, u''(t) âˆˆ -F(t, u(t), u'(t)) for a.e. t âˆˆ (a, b) l(u) = 0.