共查询到20条相似文献,搜索用时 15 毫秒
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Let X be a uniformly convex and uniformly smooth real Banach space with dual space X*. Let F: X → X* and K: X* → X be bounded monotone mappings such that the Hammerstein equation u + KFu = 0 has a solution. An explicit iteration sequence is constructed and proved to converge strongly to a solution of this equation. 相似文献
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Klaus-Jürgen Eckardt 《Mathematische Zeitschrift》1974,139(2):105-131
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Donal O'Regan 《Applicable analysis》2013,92(7):1151-1157
In this article we establish some multiplicity results for Hammerstein integral equations. The main results are based on critical point methods. 相似文献
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Robert Stadler 《Journal of Mathematical Analysis and Applications》2010,371(2):638-648
We develop relative oscillation theory for one-dimensional Dirac operators which, rather than measuring the spectrum of one single operator, measures the difference between the spectra of two different operators. This is done by replacing zeros of solutions of one operator by weighted zeros of Wronskians of solutions of two different operators. In particular, we show that a Sturm-type comparison theorem still holds in this situation and demonstrate how this can be used to investigate the number of eigenvalues in essential spectral gaps. Furthermore, the connection with Krein's spectral shift function is established. As an application we extend a result by K.M. Schmidt on the finiteness/infiniteness of the number of eigenvalues in essential spectral gaps of perturbed periodic Dirac operators. 相似文献
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Gerald Teschl 《Proceedings of the American Mathematical Society》1998,126(6):1685-1695
Oscillation theory for one-dimensional Dirac operators with separated boundary conditions is investigated. Our main theorem reads: If and if solve the Dirac equation , (in the weak sense) and respectively satisfy the boundary condition on the left/right, then the dimension of the spectral projection equals the number of zeros of the Wronskian of and . As an application we establish finiteness of the number of eigenvalues in essential spectral gaps of perturbed periodic Dirac operators.
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L. Tzafriri 《Israel Journal of Mathematics》1966,4(1):62-64
Conditions are given under which a Rellich’s perturbation theorem for normal operators on Hilbert spaces may be generalized
for spectral operators on Banach spaces. 相似文献
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《Applied mathematics and computation》2001,117(2-3):241-249
An ordinary differential equation with a parameter in the boundary conditions describes the steady state in an adiabatic tubular chemical reactor. In this paper, the problem is considered as a Hammerstein integral equation and solutions are obtained using Adomian's decomposition method. 相似文献
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