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We consider nonlinear Sturm-Liouville problems with spectral parameter in the boundary condition. We investigate the structure of the set of bifurcation points, and study the behavior of two families of continua of nontrivial solutions of this problem contained in the classes of functions having oscillation properties of the eigenfunctions of the corresponding linear problem, and bifurcating from the points and intervals of the line of trivial solutions.

Spectra of partial integral operators with a kernel of three variables

Yusup Eshkabilov (2008)

Open Mathematics

Let Ω= [a, b] × [c, d] and T 1, T 2 be partial integral operators in $C$ (Ω): (T 1 f)(x, y) = $\int_{a}^{b}$ k 1(x, s, y)f(s, y)ds, (T 2 f)(x, y) = $\int_{c}^{d}$ k 2(x, ts, y)f(t, y)dt where k 1 and k 2 are continuous functions on [a, b] × Ω and Ω × [c, d], respectively. In this paper, concepts of determinants and minors of operators E−τT 1, τ ∈ ℂ and E−τT 2, τ ∈ ℂ are introduced as continuous functions on [a, b] and [c, d], respectively. Here E is the identical operator in C(Ω). In addition, Theorems on the spectra of bounded...

Spectral Properties and Asypmtotic Behavior of the Linear Transport Equation.

Günther Greiner (1984)

Mathematische Zeitschrift

Spectral Properties of the Cauchy Operator and the Operator of Logarithmic Potential Type on L2 Space With Radial Weight

Milutin Dostanić (1998)

Matematički Vesnik

Spectral Radius Properties for Layer Potentials Associated with the Elsastostatics and Hydrostatics Equations in Nonsmooth Domains.

Irina Mitrea (1999)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

Spectre du noyau intégral ${(x^{2} + y^{2} + 1)}^{- 1}$

Michel Gaudin (1981)

Annales de l'institut Fourier

On construit les fonctions propres sur $R$ et les valeurs caractéristiques $λ_{n}$ du noyau de Hilbert-Schmidt $(x^{2} + y^{2} + 1)^{- 1}$ . Le spectre est donné par la solution d’une équation transcendante dont le comportement asymptotique est $λ_{n} ≃ \frac{1}{2} exp (π \sqrt{n})$ .

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