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Complex analytic theory of Sturm-Liouville operators with Schatten $p$-class resolvents [PDF]
Guglielmo Fucci +2 more
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2014
In Theorem 23.6, the bifurcation theorem for nonlinear Sturm–Liouville eigenvalue problems Lu = F (sBC) that concluded the previous chapter, a key hypothesis was the invertibility of \(Lu = -(pu')' + qu\) with respect to the given boundary conditions. Certainly a necessary condition for an operator to be invertible is that it be one-to-one.
Brown Robert F, Robert F Brown
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In Theorem 23.6, the bifurcation theorem for nonlinear Sturm–Liouville eigenvalue problems Lu = F (sBC) that concluded the previous chapter, a key hypothesis was the invertibility of \(Lu = -(pu')' + qu\) with respect to the given boundary conditions. Certainly a necessary condition for an operator to be invertible is that it be one-to-one.
Brown Robert F, Robert F Brown
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Complex Analysis and Operator Theory, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ferreira, M. +2 more
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ferreira, M. +2 more
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Sturm--Liouville theory for the p-Laplacian
Studia Scientiarum Mathematicarum Hungarica, 2003A version of Sturm--Liouville theory is given for the one-dimensional p-Laplacian including the radial case. The treatment is modern but follows the strategy of Elbert's early work. Topics include a Prüfer-type transformation, eigenvalue existence, asymptotics and variational principles, and eigenfunction oscillation.
Binding, P., Drábek, P.
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The Qualitative Sturm–Liouville Theory on Spatial Networks
Journal of Mathematical Sciences, 2004The authors consider boundary value problems generated by the differential expression \[ -(p(x)y')'+q(x)y=f(x) \] on the edges of a graph domain. At the pendant vertices Dirichlet boundary conditions and at the vertices of degree greater 1 the continuity conditions together with Kirchhoff-type conditions are imposed.
Pokornyi, Yu. V., Pryadiev, V. L.
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SOME PROBLEMS IN THE THEORY OF A STURM-LIOUVILLE EQUATION
Russian Mathematical Surveys, 1960CONTENTSIntroductionChapter One. The solution of the Cauchy problem for the one dimensional wave equation § 1. The application of the method of successive approximations § 2. Reduction to the Goursat problem § 3. The solution of the mixed problem on the half line § 4. The solution of a mixed problem on a finite intervalChapter Two.
Levitan, B. M., Sargsjan, I. S.
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1990
1. In a series of articles dating from 1836–1837, Sturm and Liouville created a whole new subject in mathematical analysis. The theory, later known as Sturm-Liouville theory, deals with the general linear second-order differential equation $$(k(x)V'(x))' + (g(x)r - l(x))V(x) = 0\quad for\;x \in (\alpha ,\beta ),$$ (1) with the imposed ...
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1. In a series of articles dating from 1836–1837, Sturm and Liouville created a whole new subject in mathematical analysis. The theory, later known as Sturm-Liouville theory, deals with the general linear second-order differential equation $$(k(x)V'(x))' + (g(x)r - l(x))V(x) = 0\quad for\;x \in (\alpha ,\beta ),$$ (1) with the imposed ...
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Sturm Liouville eigenvalue theory
2014In this chapter we deal with Dirichlet boundary value problems as $$\left\{ {\begin{array}{*{20}{r}} {\begin{array}{*{20}{c}} {x''\left( t \right) + A\left( t \right)x'\left( t \right) + B\left( t \right) + x\left( t \right) + \lambda C\left( t \right)x\left( t \right)}&{ = 0} \end{array}}\\ {\begin{array}{*{20}{c}} {x\left( a \right)}&{ = 0} \end ...
Shair Ahmad, Antonio Ambrosetti
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1997
In diesem Kapitel werden wir Anfangs- und Randwertprobleme fur eine lineare gewohnliche Differentialgleichung 2. Ordnung mit variablen Koeffizienten in eine Integralgleichung umformen, sodas wir die Ergebnisse (insbesondere uber Eigenwerte) aus Kapitel 2 und 4 benutzen konnen. Auf einem Intervall [a, b] betrachten wir die Gleichung $$\bar{p}(s){x}''
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In diesem Kapitel werden wir Anfangs- und Randwertprobleme fur eine lineare gewohnliche Differentialgleichung 2. Ordnung mit variablen Koeffizienten in eine Integralgleichung umformen, sodas wir die Ergebnisse (insbesondere uber Eigenwerte) aus Kapitel 2 und 4 benutzen konnen. Auf einem Intervall [a, b] betrachten wir die Gleichung $$\bar{p}(s){x}''
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Sturm–Liouville Theory and its Applications
Springer Undergraduate Mathematics Seriesopenaire +3 more sources