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Some global results for nonlinear Sturm-Liouville problems with spectral parameter in the boundary condition

Ziyatkhan S. Aliyev, Gunay M. Mamedova (2015)

Annales Polonici Mathematici

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) = a b k 1(x, s, y)f(s, y)ds, (T 2 f)(x, y) = 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...

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 1 2 exp ( π n ) .

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