Erratum to Spectral exactness and spectral inclusion for singular left definite Sturm-Liouvelle problems
نویسندگان
چکیده
منابع مشابه
Direct and inverse spectral theory of singular left-definite Sturm–Liouville operators
We discuss direct and inverse spectral theory of self-adjoint Sturm– Liouville relations with separated boundary conditions in the left-definite setting. In particular, we develop singular Weyl–Titchmarsh theory for these relations. Consequently, we apply de Branges’ subspace ordering theorem to obtain inverse uniqueness results for the associated spectral measure. The results can be applied to...
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Abstract: This paper deals with the boundary value problem involving the differential equation -y''+q(x)y=lambda y subject to the standard boundary conditions along with the following discontinuity conditions at a point y(a+0)=a1y(a-0), y'(a+0)=a2y'(a-0)+a3y(a-0). We develop the Hochestadt-Lieberman’s result for Sturm-Lio...
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Left-definite regular self-adjoint Sturm-Liouville problems with separated and coupled boundary conditions are studied. A characterization is given in terms of right-definite problems, a concrete and “natural” indexing scheme for the eigenvalues is proposed. Pruefer transformation techniques can be used to establish the existence of and to give a characterization for the eigenvalues in the case...
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together with appropriate boundary conditions, in the space Lw of functions square integrable with respect to the weight w, i.e., the normsquare of the space is ‖u‖2 = ∫ |u|2w. A basic assumption for this to be possible is that w ≥ 0. In some situations of interest this is not the case, but instead one has p > 0, q ≥ 0. One may then use as a norm-square the integral ∫ (p|u′|2 + q|u|2), and a pr...
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This paper concerns the nonlinear Sturm-Liouville problem −u′′(t) + f(u(t)) = λu(t), u(t) > 0, t ∈ I := (0, 1), u(0) = u(1) = 0, where λ is a positive parameter. We try to determine the nonlinear term f(u) by means of the global behavior of the bifurcation branch of the positive solutions in R+ × L2(I).
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ژورنال
عنوان ژورنال: Results in Mathematics
سال: 2005
ISSN: 0378-6218,1420-9012
DOI: 10.1007/bf03323022