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Original Articles

Positive solutions of a nonlinear elliptic equationFootnote

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Pages 179-187 | Published online: 29 May 2007

References

  • Atkinson , F. V. and Peletier , L. A. 1988 . Large solutions of elliptic equations involving critical exponents . Asymptotic Analysis , 1 : 139 – 160 .
  • Brezis , H. and Nirenberg , L. 1983 . Positive solutions of nonlinear elliptic equations involving critical sobolev exponents . Comm. Pure Appl. Math. , 36 : 437 – 477 .
  • Coffman , C. V. 1972 . Uniqueness of the ground state solution for ▵u - u + u 3 = 0 and a variational characterization of other solutions . Arch. Rational Mech. Anal. , 46 : 81 – 95 .
  • Gidas , B. , Ni , W. M. and Nirenberg , L. 1979 . Symmetry and related properties via the maximum principle . Comm. Math. Phys. , 68 : 209 – 243 .
  • Gidas , B. , Ni , W. M. and Nirenberg , L. 1981 . Symmetry of positive solutions of nonlinear elliptic equations in . Math. Anal. Appl. Adv. in Math. Suppl. Stud. , 7A : 369 – 402 .
  • Hartman , P. 1964 . Ordinary Differential Equations, J. , New York : Wiley and Sons .
  • Jones , C. K. R. T. 1988 . Radial solutions of a semilinear elliptic equation at a critical exponent . Arch. Rational Mech. Anal. , 104 : 251 – 270 .
  • Kwong , M. K. 1989 . Uniqueness of positive solutions of . Arch. Rational Mech. Anal. , 105 : 243 – 266 .
  • Lions , P. L. 1982 . On the existence of positive solutions of semilinear elliptic equations . SIAM Reviews , 24 : 441 – 467 .
  • McLeod , K. and Serrin , J. 1981 . Uniqueness of solutions of semilinear Poisson equations . Proc. Natl. Acad. Sci. USA , 78 : 6592 – 6595 .
  • Ni , W. M. 1983 . Uniqueness of solutions of nonlinear Dirichlet problems . J. Differential Equations , 50 : 289 – 304 .
  • Payne , L. E. 1988 . “ Some special maximum principles with applications to isoperimetric inequalities ” . In Maximum Principles and Eigenvalue Problems in Partial Differential Equations , New York : John Wiley & Sons .
  • Peletier , L. A. and Serrin , J. 1983 . Uniqueness of positive solutions of semilinear equations in . Arch. Rational Mech. Anal , 81 : 181 – 197 .
  • Peletier , L. A. and Serrin , J. 1986 . Uniqueness of positive solutions of semilinear equations in [ILM00010] . J. Differential Equations , 61 : 380 – 397 .
  • Pohozaev , S. I. 1965 . Eigenfunctions of the equation ▵u + λf(u) = 0 . Soviet Math. Doklady , 6,165 : 1408,33 – 1411,36 . (translated from the Russian Dokl. 1965 Akad. Nauk SSSR
  • Zhang , D. 1989 . On multiple solutions of . Nonlinear Analysis , 13 : 353 – 372 .

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