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A nonlinear perturbation ofd 2 u/dx 2u,u(−∞)=u+∞)=0

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The question of existence of solutions vanishing at infinity for a class of second order ordinary differential equations in L1(R)is analyzed.


  1. [1]

    A. Ambrosetti -G. Prodi,On the inversion of some differentiable mappings with singularities between Banach spaces, Ann. Mat. Pura Appl.,93 (1972), pp. 231–246.

  2. [2]

    P. Benilan -H. Brezis -M. Crandall,A senvilinear equation in L 1(R n), Ann. Scuola Norm. Sup. Pisa, Serie IV,2 (1975), pp. 523–555.

  3. [3]

    M. S.Berger,Nonlinearity and Functional Analysis, Academic Press, 1977.

  4. [4]

    R. E.Edwards,Functional Analysis, Holt, Rinehart & Winston, 1965.

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Ortega, R. A nonlinear perturbation ofd 2 u/dx 2u,u(−∞)=u+∞)=0. Annali di Matematica pura ed applicata 152, 159–169 (1988). https://doi.org/10.1007/BF01766146

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  • Differential Equation
  • Ordinary Differential Equation
  • Order Ordinary Differential Equation
  • Nonlinear Perturbation