Publication Cover
Applicable Analysis
An International Journal
Volume 86, 2007 - Issue 7
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Original Articles

On the shape of level sets of least energy solutions to some elliptic problems with nearly critical growth

Pages 851-859 | Received 19 Mar 2007, Accepted 18 May 2007, Published online: 27 Sep 2007

References

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  • Gladiali , F and Grossi , M . 2004 . Strict convexity of level sets of solutions of some nonlinear elliptic equations . Proceedings of the Royal Society of Edinburgh , 134A : 363 – 373 .
  • Gladiali , F and Grossi , M . 2004 . Some results on the Gel’fand problem . Communications in Partial Differential Equations , 29 : 1335 – 1364 .
  • Grossi , M and Molle , R . 2003 . On the shape of the solutions of some semilinear elliptic problems . Communications in Contemporary Mathematics , 5 : 85 – 99 .
  • Hebey , E . 2000 . Asymptotic behavior of positive solutions of quasilinear elliptic equations with critical Sobolev growth . Differential and Integral Equations , 13 : 1073 – 1080 .
  • Pohozaev , S . Eigenfunctions of the equation Δu = λf(u). . Soviet Mathematics Doklady , 6 1408 – 1411 .
  • Han , ZC . 1991 . Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent . Annales de l’Institut Henri Poincaré , 8 : 159 – 174 .
  • Rey , O . 1989 . Proof of two conjectures of H. Brezis, and L.A. Peletier . Manuscripta Mathematica , 65 : 19 – 37 .
  • Rey , O . 1990 . The role of the Green's function in a non-linear elliptic equation involving the critical Sobolev exponent . Journal of Functional Analysis , 89 : 1 – 52 .
  • Sato , T and Suzuki , T . 2005 . Convexity and uniqueness of the solution to the Liouville equation . Interernational Journal of Pure and Applied Mathematics , 23 : 1 – 21 .

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