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On a nonlinear ordinary differential equation

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Literature cited

  1. Z. Nehari, “On a nonlinear differential equation arising in nuclear physics,”Proc. Royal Irish. Acad.,62, Sect. A, 117–135 (1963).

    Google Scholar 

  2. E. P. Zhidkov and V. P. Shirikov, “On a boundary-value problem for second-order ordinary differential equations,”Zh. Vychisl. Mat. Mat. Fiz.,4, No. 5, 804–816 (1964).

    Google Scholar 

  3. G. H. Ryder, “Boundary value problems for a class of nonlinear differential equations,”Pacif. J. Math.,22, No. 3, 477–503 (1967).

    Google Scholar 

  4. E. P. Zhidkov, V. P. Shirikov, and I. V. Pusynin, “The Cauchy problem and boundary value problem for a second-order nonlinear ordinary differential equation,” In: JINR Report No. 2005, Dubna (1965).

  5. G. Sansone, “Su un equazione non linear della fisica nucleare,”Symposia Math.,6, 3–139 (1971).

    Google Scholar 

  6. J. W. Macry, “A singular nonlinear boundary value problem,”Pacif. J. Math.,78, No. 2, 375–383 (1978).

    Google Scholar 

  7. H. Berestycki and P. L. Lions, “Existence d'ondes solitaires dens des problems nonlinear du type Klein-Gordon,”C. R. Acad. Sci.,AB 288, No. 7, 395–398 (1979).

    Google Scholar 

  8. H. Berestycki, P. L Lions, and L. A. Peletier, “An QDE approach to the existence of positive solutions for semilinear problems in ℝN,”Indiana Univ. Math. J.,30, No. 1, 142–157 (1981).

    Article  Google Scholar 

  9. I. T. Kiguradze and B. L. Shekhter, “Singular boundary-value problems for second-order ordinary differential equations,”Sovrem. Problem. Matem. (Modern Problems of Mathematics),30, 105–201 (1987).

    Google Scholar 

  10. Ch. V. Goffman, “Uniqueness of the ground state solution for Δu−u+u 3=0 and a variational characterization of other solutions,”Arch. Rational Mech. Anal.,46, 81–95 (1972).

    Google Scholar 

  11. K. McLeod and J. Serrin, “Uniqueness of solutions of semilinear Poisson equations,”Proc. Nat. Sci. USA,78, No. 11, 6592–6595 (1981).

    Google Scholar 

  12. L. A. Peletier and J. Serrin, “Uniqueness of non-negative solutions of semilinear equations in ℝN,”J. Diff. Eq.,61, No. 3, 380–397 (1986).

    Article  Google Scholar 

  13. M. K. Kwong, “Uniqueness of positive solutions of Δu−u+u p=0 in ℝN,”Arch. Rational Mech. Anal.,105, No. 3, 243–266 (1989).

    Article  Google Scholar 

  14. S. I. Pokhozhaev, “On eigenfunctions of the equation Δu+λf(u)=0,”Dokl. Akad. Nauk SSSR,165, No. 1, 36–39 (1965).

    Google Scholar 

  15. P. E Zhidkov, “On uniqueness of particle-similar solutions with an arbitrary given number of nodes,”Vestnik Moskov. Univ., Ser. 15., Vych. Mat. Kibern., No. 4, 12–16 (1983).

    Google Scholar 

  16. D. Mikhalake, R. G. Nazmitdinov, and V. K. Fedianin, “Nonlinear optical waves in laminated structures,”Fiz. Elem. Chastits Atom. Yad.,20, No. 1, 198–253 (1982).

    Google Scholar 

  17. E. P. Zhidkov and P. E. Zhidkov, “Investigation of particle-similar solutions in some models of nonlinear physics,” In: JINR Reports No. I 5-12609, 5-12610, Dubna (1979).

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Translated from Matematicheskie Zametki, Vol. 55, No. 4, pp. 25–34, April, 1994.

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Zhidkov, P.E., Sakbaev, V.Z. On a nonlinear ordinary differential equation. Math Notes 55, 351–357 (1994). https://doi.org/10.1007/BF02112473

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