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Dokl. Akad. Nauk SSSR, 1965, Volume 165, Number 1, Pages 36–39 (Mi dan31757)  

This article is cited in 32 scientific papers (total in 33 papers)


Eigenfunctions of the equation $\Delta u+\lambda f(u)=0$

S. I. Pokhozhaev

Moscow Power Engineering Institute

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Document Type: Article
UDC: 517.946.4
Presented: I. G. Petrovskii
Received: 23.03.1965

Citation: S. I. Pokhozhaev, “Eigenfunctions of the equation $\Delta u+\lambda f(u)=0$”, Dokl. Akad. Nauk SSSR, 165:1 (1965), 36–39

Citation in format AMSBIB
\by S.~I.~Pokhozhaev
\paper Eigenfunctions of the equation $\Delta u+\lambda f(u)=0$
\jour Dokl. Akad. Nauk SSSR
\yr 1965
\vol 165
\issue 1
\pages 36--39

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    This publication is cited in the following articles:
    1. V. S. Klimov, “On imbedding theorems for symmetric spaces”, Math. USSR-Sb., 11:3 (1970), 339–353  mathnet  crossref  mathscinet  zmath
    2. V. G. Maz'ya, T. O. Shaposhnikova, “Theory of multipliers in spaces of differentiable functions”, Russian Math. Surveys, 38:3 (1983), 23–95  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. M. I. Vishik, S. B. Kuksin, “Perturbations of quasilinear elliptic equations and Fredholm manifolds”, Math. USSR-Sb., 58:1 (1987), 223–243  mathnet  crossref  mathscinet  zmath
    4. M. V. Vladimirov, “Solvability of a mixed problem for the nonlinear Schrödinger equation”, Math. USSR-Sb., 58:2 (1987), 525–540  mathnet  crossref  mathscinet  zmath
    5. S. I. Pokhozhaev, “On elliptic problems in $\mathbf R^N$ with supercritical exponent of nonlinearity”, Math. USSR-Sb., 72:2 (1992), 447–466  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. Ya. Sh. Il'yasov, “On the existence of periodic solutions of semilinear elliptic equations”, Russian Acad. Sci. Sb. Math., 79:1 (1994), 167–178  mathnet  crossref  mathscinet  zmath  isi
    7. S. I. Pokhozhaev, “Sharp a priori estimates for a quasilinear degenerate elliptic problem”, Russian Acad. Sci. Sb. Math., 79:2 (1994), 335–346  mathnet  crossref  mathscinet  zmath  isi
    8. A. P. Buslaev, “Some properties of the spectrum of nonlinear equations of Sturm–Liouville type”, Russian Acad. Sci. Sb. Math., 80:1 (1995), 1–14  mathnet  crossref  mathscinet  zmath  isi
    9. P. E. Zhidkov, V. Zh. Sakbaev, “On a nonlinear ordinary differential equation”, Math. Notes, 55:4 (1994), 351–357  mathnet  crossref  mathscinet  zmath  isi
    10. Ya. Sh. Il'yasov, “On function of action on the manifold of ground state solutions”, Theoret. and Math. Phys., 105:3 (1995), 1546–1555  mathnet  crossref  mathscinet  zmath  isi  elib
    11. Ya. Sh. Il'yasov, “An equation that arises in studying ground state solutions to semilinear elliptic equations”, Math. Notes, 58:3 (1995), 996–1000  mathnet  crossref  mathscinet  zmath  isi
    12. Ya. Sh. Il'yasov, “On periodic non-trivial solutions of the equation $-\Delta u=g(u)$ in $\mathbb R^{N+1}$”, Izv. Math., 59:1 (1995), 101–119  mathnet  crossref  mathscinet  zmath  isi
    13. A. B. Aliev, A. Kh. Khanmamedov, “Energy estimates for solutions of the mixed problem for linear second-order hyperbolic equations”, Math. Notes, 59:4 (1996), 345–349  mathnet  crossref  crossref  mathscinet  zmath  isi
    14. I. A. Kuzin, “Absence of a countable set of solutions for certain elliptic problems with right-hand side and with supercritical nonlinearity exponent”, Math. Notes, 60:3 (1996), 337–341  mathnet  crossref  crossref  mathscinet  zmath  isi
    15. O. V. Besov, V. I. Il'in, L. D. Kudryavtsev, V. P. Kurdyumov, S. M. Nikol'skii, L. V. Ovsyannikov, V. A. Sadovnichii, “Stanislav Ivanovich Pokhozhaev (on his sixtieth birthday)”, Russian Math. Surveys, 51:2 (1996), 363–369  mathnet  crossref  crossref  mathscinet  zmath  isi
    16. Nguyen Minh Tri, “On Grushin's equation”, Math. Notes, 63:1 (1998), 84–93  mathnet  crossref  crossref  mathscinet  zmath  isi
    17. M. O. Korpusov, A. G. Sveshnikov, “Blowup in a finite time of the solution to the initial-boundary value problem for a semilinear composite type equation”, Comput. Math. Math. Phys., 40:11 (2000), 1647–1654  mathnet  mathscinet  zmath
    18. S. I. Pokhozhaev, “A General Approach to the Theory of Nonexistence of Global Solutions to Nonlinear Partial Differential Equations and Inequalities”, Proc. Steklov Inst. Math., 236 (2002), 273–284  mathnet  mathscinet  zmath
    19. Boris V. Trushin, “Embedding of the Sobolev Space into the Orlicz and BMO Spaces with Power Weights”, Proc. Steklov Inst. Math., 243 (2003), 323–334  mathnet  mathscinet  zmath
    20. I. G. Tsar'kov, “Nonunique Solvability of Certain Differential Equations and Their Connection with Geometric Approximation Theory”, Math. Notes, 75:2 (2004), 259–271  mathnet  crossref  crossref  mathscinet  zmath  isi
    21. Proc. Steklov Inst. Math., 255 (2006), 234–243  mathnet  crossref  mathscinet
    22. I. G. Tsar'kov, “Stability of Unique Solvability in an Ill-Posed Dirichlet Problem”, Math. Notes, 79:2 (2006), 268–282  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    23. D. P. Kostomarov, S. Yu. Medvedev, D. Yu. Sychugov, “Methods for MHD plasma equilibria mathematical modelling”, Math. Models Comput. Simul., 1:2 (2009), 228–254  mathnet  crossref  mathscinet  zmath
    24. E. I. Abduragimov, “Uniqueness of a positive radially symmetric solution in a ball to the Dirichlet problem for one nonlinear differential equation of the second order”, Russian Math. (Iz. VUZ), 52:12 (2008), 1–3  mathnet  crossref  mathscinet  zmath
    25. M. Kh. Chankaev, A. B. Shabat, “A nonlinear eigenvalue problem”, Theoret. and Math. Phys., 157:2 (2008), 1514–1524  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    26. H. Zou, “A priori estimates, existence and non-existence for quasilinear cooperative elliptic systems”, Sb. Math., 199:4 (2008), 557–578  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    27. M. O. Korpusov, “On the uniqueness of the solution of a nonlinear eigenmode problem”, Comput. Math. Math. Phys., 51:4 (2011), 597–601  mathnet  crossref  mathscinet  isi  elib
    28. M. O. Korpusov, A. G. Sveshnikov, “On a nonlinear eigenmode problem in semiconductor theory”, Comput. Math. Math. Phys., 51:5 (2011), 816–823  mathnet  crossref  mathscinet  isi  elib
    29. E. I. Abduragimov, “Uniqueness of a positive solution to the Dirichlet problem for a quasilinear equation with $p$-Laplacian in a ball”, Russian Math. (Iz. VUZ), 55:10 (2011), 1–8  mathnet  crossref  mathscinet
    30. L. S. Efremova, V. Zh. Sakbaev, “Notion of blowup of the solution set of differential equations and averaging of random semigroups”, Theoret. and Math. Phys., 185:2 (2015), 1582–1598  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
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    32. Ya. Sh. Il'yasov, “On the curve of critical exponents for nonlinear elliptic problems in the case of a zero mass”, Comput. Math. Math. Phys., 57:3 (2017), 497–514  mathnet  crossref  crossref  isi  elib
    33. T. V. Dudnikova, “Virial identities and energy-momentum relation for solitary waves of nonlinear Dirac equations”, Preprinty IPM im. M. V. Keldysha, 2018, 012, 36 pp.  mathnet  crossref
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