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 Pavlenko A.N. ABOUT SOLUTIONS OF OPERATOR EQUATION U=KW(U, λ)In this article we prove existence no less two solutions of operator equation u=KW(u, λ), that is the generalization of the results got for operator equation u=λKW(u) and for its several individualizings.Key words: operator equation, cone, rotation of fully continuous vector field, homotopic vector fields, index of singular point.
References:
 1. Klimov, V.S. One-dimensional boundary problems with two solutions. // Qualitative and approximating methods or research of operator equations. Issue 3. Yaroslavl, 1978. — P. 90-111. 2. Klimov, V.S., Pavlenko, A. N. Nontrivial solutions of boundary problems with powerful nonlinearities // Differential Equations, №12, 1997. V. 30. P. 1676-1682. 3. Pavlenko, A.N. Inverse functional inequalities and their applications. Thesis of candidate of physical-mathematical sciences: 01.01.02. — Voronezh: VSU, 1998. — 117 p. 4. Klimov, V.S., Pavlenko, A. N. Inverse functional inequalities for vector functions of scalar argument and their application to nonlinear elliptical boundary problems // Siberian mathematical magazine. №4, 2001. V. 42. P. 781-795. 5. Pavlenko, A.N. Inverse functional inequalities for vector functions of scalar argument and their application to nonlinear boundary problems // Vestnik of the Orenburg State University. October 2008. №10 (92). P. 128-134. 6. Functional analysis (Reference mathematical literature.) / edited by S. G. Kreyn. — Moscow: Nauka, 1972. — 544 p. 7. Krasnoselskiy, M.A. Positive linear systems: method of the positive operators / M. A. Krasnoselskiy, E. A., E. A. Lifshits, A.V. Sobolev. — Moscow: Nauka, 1985. — 256 p. 8. Krasnoselskiy, M.A. Geometric methods of the nonlinear analysis / M. A. Krasnoselskiy, P. P. Zabreyko. — Moscow: Nauka, 1975. — 510 p. 
 About this articleAuthor: Pavlenko A.N.
 Year: 2010
 
 
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|  Editor-in-chief
 |  | Sergey Aleksandrovich MIROSHNIKOV
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