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Eigenvalue estimates for Fourier concentration operators on two domains. [PDF]
Arch Ration Mech AnalMarceca F, Romero JL, Speckbacher M.
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On an Inverse Problem for Sturm-Liouville Equation
, 2017 Döne Karahan, Khanlar R. Mamedov
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Indefinite Sturm–Liouville problems
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2003We study the spectrum of regular and singular Sturm–Liouville problems with real-valued coefficients and a weight function that changes sign. The self-adjoint boundary conditions may be regular or singular, separated or coupled. Sufficient conditions are found for (i) the spectrum to be real and unbounded below as well as above and (ii) the essential ...
Kong, Q., Wu, H., Zettl, A., Möller, M.
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2020
In Chap. 3 we have seen how the separability of PDEs leads to ordinary differential equations problems, usually of second order. The problem is complemented with B.C.s and the reduction of the initial PDE to second order ODEs often yield a so-called Sturm–Liouville (SL) problem (named after the French mathematicians Jacques Charles Francois Sturm, 1803–
Cossali G., Tonini S.
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In Chap. 3 we have seen how the separability of PDEs leads to ordinary differential equations problems, usually of second order. The problem is complemented with B.C.s and the reduction of the initial PDE to second order ODEs often yield a so-called Sturm–Liouville (SL) problem (named after the French mathematicians Jacques Charles Francois Sturm, 1803–
Cossali G., Tonini S.
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2015
The chapter provides an existence principle for the Sturm–Liouville boundary value problem with p (\(p \in \mathbb {N}\)) state-dependent impulse conditions Open image in new window Provided a, \(b \in [0,\infty )\), \(c_j \in \mathbb {R}\), \(j = 1,2\), and the data functions f, \(J_i\), \(M_i\), \(i=1,\ldots ,p\), are bounded ...
Irena Rachůnková, Jan Tomeček
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The chapter provides an existence principle for the Sturm–Liouville boundary value problem with p (\(p \in \mathbb {N}\)) state-dependent impulse conditions Open image in new window Provided a, \(b \in [0,\infty )\), \(c_j \in \mathbb {R}\), \(j = 1,2\), and the data functions f, \(J_i\), \(M_i\), \(i=1,\ldots ,p\), are bounded ...
Irena Rachůnková, Jan Tomeček
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Nonlinear singular Sturm–Liouville problems
Nonlinear Analysis: Theory, Methods & Applications, 1999Singular Sturm-Liouville differential equations of the form \[ -(r(t)u')'+p(t)u=f(t,u),\quad t \in(a,b), \] associated with boundary conditions of Dirichlet type are considered. In [\textit{C. de Coster, M. R. Grossinho} and \textit{P. Habets}, Appl. Anal. 59, No.
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Stochastic nonhomogeneous sturm liouville problems
Journal of the Franklin Institute, 1966Abstract Nonhomogeneous boundary value problems of the Sturm-Liouville type having random forcing functions are considered. Estimates for the statistical moments of the response are found in the case that the forcing function is stationary and weakly correlated, thereby extending previous work having to do with stochastic initial value problems.
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Strongly Singular Sturm - Liouville Problems
Mathematische Nachrichten, 2001In the usual Sturm-Liouville theory, in order to use the spectral theorem for selfadjoint operators in Hilbert spaces, appropriate boundary conditions are used together with the Sturm-Liouville equation \[ -(ru'(x))'+ p(x) u(x)=\lambda m(x) u(x)\quad\text{on }(a,b) \] to form selfadjoint eigenvalue problems. For example, for the Fourier equation \(-u''=
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Nonlinear multiparameter Sturm–Liouville problems
Asymptotic Analysis, 1998An asymptotic formula of variational eigenvalues of nonlinear multiparameter Sturm–Liouville problems is established. The proof is based on Ljusternik–Schnirelman theory on general level sets due to Zeidler, Pohozaev‐type equality and ODE techniques.
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