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Matematicheskie Zametki, 1969, Volume 5, Issue 2, Pages 253–260 (Mi mzm6830)  
This article is cited in 6 scientific papers (total in 6 papers)

Non-zero solutions of equations with strong nonlinearities

M. A. Krasnosel'skiiab, Yu. V. Pokornyiab

a Voronezh State University
b Automatics and Mechanics (Technical Cybernetics) Institute of USSR Academy of Sciences
Full-text PDF (600 kB) Citations (6)
Abstract: Existence theorems are proved for non-zero solutions of a multi-point Valle–Poussin boundary problem for differential equations with strong non-linearities. The proof is based on the construction of special cones in a Banach space, and on the application of a modification of a theorem on fixed points of operators which expand a cone.
Received: 04.03.1968
English version:
Mathematical Notes, 1969, Volume 5, Issue 2, Pages 153–157
DOI: https://doi.org/10.1007/BF01098316
Bibliographic databases:
UDC: 513.88
Language: Russian
Citation: M. A. Krasnosel'skii, Yu. V. Pokornyi, “Non-zero solutions of equations with strong nonlinearities”, Mat. Zametki, 5:2 (1969), 253–260; Math. Notes, 5:2 (1969), 153–157
Citation in format AMSBIB
\Bibitem{KraPok69}
\by M.~A.~Krasnosel'skii, Yu.~V.~Pokornyi
\paper Non-zero solutions of equations with strong nonlinearities
\jour Mat. Zametki
\yr 1969
\vol 5
\issue 2
\pages 253--260
\mathnet{http://mi.mathnet.ru/mzm6830}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=240687}
\zmath{https://zbmath.org/?q=an:0183.15601}
\transl
\jour Math. Notes
\yr 1969
\vol 5
\issue 2
\pages 153--157
\crossref{https://doi.org/10.1007/BF01098316}
Linking options:
  • https://www.mathnet.ru/eng/mzm6830
  • https://www.mathnet.ru/eng/mzm/v5/i2/p253
    • This publication is cited in the following 6 articles:
    1. G. E. Abduragimov, “O suschestvovanii polozhitelnogo resheniya kraevoi zadachi dlya odnogo nelineinogo funktsionalno-differentsialnogo uravneniya vtorogo poryadka”, Materialy Mezhdunarodnoi konferentsii  «Klassicheskaya i sovremennaya geometriya»,  posvyaschennoi 100-letiyu so dnya rozhdeniya  professora Levona Sergeevicha Atanasyana  (15 iyulya 1921 g.—5 iyulya 1998 g.). Moskva, 1–4 noyabrya 2021 g. Chast 2, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 221, VINITI RAN, M., 2023, 3–9  mathnet  crossref
    2. G. E. Abduragimov, “Existence and uniqueness of positive solution to a boundary value problem for a nonlinear second order functional-differential equation”, Russian Math. (Iz. VUZ), 64:12 (2020), 1–5  mathnet  crossref  crossref  isi
    3. Yu. V. Pokornyi, “Zeros of the Green's function for the de la Vallée-Poussin problem”, Sb. Math., 199:6 (2008), 891–921  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. Jairo Santanilla, “Existence and nonexistence of positive radial solutions for some semilinear elliptic problems in annular domains”, Nonlinear Analysis: Theory, Methods & Applications, 16:10 (1991), 861  crossref
    5. V. S. Klimov, “Nontrivial solutions of boundary value problems for semilinear elliptic equations”, Math. USSR-Izv., 5:2 (1971), 445–457  mathnet  crossref  mathscinet  zmath
    6. P. P. Zabreiko, M. A. Krasnosel'skii, Yu. V. Pokornyi, “On a class of linear positive operators”, Funct. Anal. Appl., 5:4 (1971), 272–279  mathnet  crossref  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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