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What Do Singular Indefinites Mean in Child English?
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Singular solitons and indefinite metrics
Doklady Mathematics, 2011The singular real second order 1D Schrodinger operators are considered here with such potentials that all local solutions near singularities to the eigenvalue problem are meromorphic for all values of the spectral parameter. All algebro-geometrical or "singular finite-gap" potentials satisfy to this condition.
P. G. Grinevich, S. P. Novikov
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Periodic Solutions of an Indefinite Singular Planar Differential System
Mediterranean Journal of Mathematics, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zaitao Liang +2 more
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Positive periodic solution to an indefinite singular equation
Applied Mathematics Letters, 2021The paper is concerned with the singular equation \[ x'' + q(t)x = \frac{b(t)}{x^\rho} + e(t), \] where \(\rho > 0\) and \(q,b,e\) are \(\omega\)-periodic continuous functions, with \(q(t), e(t) > 0\) for all \(t\). Under suitable assumptions on the Green's function of the associated linear equation and on the nonlinear term, the existence of a ...
Cheng, Zhibo, Cui, Xiaoxiao
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Parametric Singular Problems with an Indefinite Perturbation
The Journal of Geometric AnalysisThe authors study parametric Dirichlet problems driven by a nonhomogenous differential operator and with parametric reaction containing singular term and a sign-changing perturbation. The main theorem of the paper establishes the existence of at least two smooth positive solutions.
Krzysztof Bień +2 more
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Singular — General — Indefinite
1974Von Freytag’s little book contains scarcely any information on the logic of logophoric terms. We therefore have no choice but to give considerable weight to his brief remarks on this topic. The reader will remember that he says: “…“der (die, das)” heisst das Element” (1961/65; cp. III-4).
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NONREAL EIGENVALUES OF SINGULAR INDEFINITE STURM–LIOUVILLE PROBLEMS
Rocky Mountain Journal of MathematicsA singular indefinite Sturm-Liouville problem \(-(py')' + q y = \lambda w y\) with \(p, |w| > 0\) a.e. is considered on a finite interval \((a, b)\) equipped with self-adjoint boundary conditions (in an indefinite sense). In case of sign changes of \(w\) there may appear nonreal eigenvalues.
Han, Xiaoxue, Sun, Fu
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Positive periodic solution to indefinite singular Liénard equation
Positivity, 2018The authors consider a scalar equation of the type \[ x''+f(x)x'+\frac{b(t)}{x}=p(t)\,, \] where \(f:{\mathbb R}\to{\mathbb R}\) is continuous, and \(b,p:{\mathbb R}\to{\mathbb R}\) are continuous and \(T\)-periodic. Under some assumptions on the functions \(b\) and \(p\), they prove the existence of a positive \(T\)-periodic solution.
Yun Xin, Zhibo Cheng
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The spectra of indefinite singular Sturm-Liouville operators
2022In der vorliegenden Arbeit werden die spektralen Eigenschaften singulärer Sturm-Liouville- Differentialoperatoren der Form Af=1/r(︁−(pf′)′ + qf)︁ mit reellwertigen Koeffizienten p, q und r untersucht. Hierbei betrachten wir indefinite Gewichtsfunktionen r.
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