Results 101 to 110 of about 262 (118)
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The Periodic Sturm–Liouville Equations
2017We begin with a brief introduction the periodic Sturm–Liouville equations \([p(x)y'(x)]' + [\lambda w(x) - q(x)] y(x) = 0\). After reviewing some elementary knowledge of the theory of a general class of second-order linear homogeneous ordinary differential equations, we introduce two basic Sturm theorems on the zeros of solutions of the equations. Then,
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Stability of solutions to Sturm-Liouville diffusion equations
Transport Theory and Statistical Physics, 1986Abstract Stability of solutions of abstract half-space problems of the type T ψ'1 (x)=-Aψ(x)(0> x > ∞) is established under perturbations of the resolvent of the (unbounded) positive self-adjoint operator A. Applications are given to Sturm-Liouville type diffusion equations.
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Inverse problem for Sturm-Liouville and hill equations
Annali di Matematica Pura ed Applicata, 1987We discuss the inverse Sturm-Liouville problem on a finite interval by the method of transformation kernel. The \(\tau\)-function, the Fredholm determinant of the transformation kernel, is explicitly written down in terms of the spectral data, from which a very explicit representation formula for the potential is deduced, and well-posedness of the ...
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A Neumann boundary value problem for the Sturm–Liouville equation
Applied Mathematics and Computation, 2009The authors deal with the Neumann boundary value problem \[ -(pu')'+ru'+qu=\lambda g(u), \;\; u'(0)=u'(1)=0,\tag{1} \] where \(p\) is a \(C^1 \) positive function in \([0,1]\), \(r\) and \(q\) are continuous in \([0,1]\), \(r\) is positive; \(\lambda \) is a positive parameter. The solutions to (1) are the critical points of a functional of the form \(\
BONANNO, Gabriele, D'AGUI', GIUSEPPINA
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DISTRIBUTION OF THE EIGENVALUES OF THE STURM-LIOUVILLE OPERATOR EQUATION
Mathematics of the USSR-Izvestiya, 1977This work contains an analysis of the dependence of the lower terms of the asymptotics of the distribution of the eigenvalues of the equation upon the spectrum of the positive selfadjoint operator and the form of the boundary conditions. As a corollary the second term is found for the spectral asymptotics of classical boundary value problems for the ...
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On the spectrum of an operator sturm — Liouville equation
Functional Analysis and Its Applications, 1972openaire +1 more source