A NOTE ON THE UNIQUENESS OF POSITIVE SOLUTIONS OF ROBIN PROBLEM*
Glasgow mathematical journal, Tome 50 (2008) no. 3, pp. 437-445

Voir la notice de l'article provenant de la source Cambridge University Press

This note is devoted to prove some uniqueness results of positive solutions of a Robin problem for semi-linear elliptic equations and systems.
DOI : 10.1017/S0017089508004321
Mots-clés : 35J25, 35J55
DAI, QIUYI; FU, YUXIA. A NOTE ON THE UNIQUENESS OF POSITIVE SOLUTIONS OF ROBIN PROBLEM*. Glasgow mathematical journal, Tome 50 (2008) no. 3, pp. 437-445. doi: 10.1017/S0017089508004321
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[1] 1.Ni, W. M. and Nussbaum, R. D., Uniqueness and non-uniqueness for positive solutions of Δ u+f(r,u)=0, Commun. Pure Appl. Math. 38 (1985), 67–108. Google Scholar | DOI

[2] 2.Dai, Q. Y., Entire positive solutions for inhomogeneous semilinear elliptic systems, Glasgow Math. J. 47 (2005), 97–114. Google Scholar

[3] 3.Dai, Q. Y., Fu, Y. X. and Gu, Y. G., Uniqueness of positive solutions of semilinear elliptic equations, Sci. China A 50 (2007), 1141–1156. Google Scholar

[4] 4.Gidas, B. and Spruck, J., A priori bounds for positive solutions of semilinear elliptic equations, Commun. Part. Differ. Equ. 6 (1981), 883–901. Google Scholar | DOI

[5] 5.Gilbarg, D. and Trudinger, N. S., Elliptic partial differential equations of second order (Springer-Velag, Berlin, Germany, 2001). Google Scholar | DOI

[6] 6.Damascelli, L., Grossi, M. and Pacella, F., Qualitative properties of positive solutions of semilinear equations in symmetric domains via maximum principle, Ann. Inst. Henri Poincare Analse non lineaire 16 (1999), 631–652. Google Scholar

[7] 7.Dancer, E. N., The effect of domain shape on the number of positive solutions of certain weakly nonlinear equations, J. Differ. Equ. 74 (1988), 120–156. Google Scholar | DOI

[8] 8.Dancer, E. N., On the influence of domain shape on the existence of large solutions of some superlinear problems, Math. Ann. 285 (1989), 647–669. Google Scholar | DOI

[9] 9.Wang, X. J., Neumann problems of semilinear elliptic equations involving critical Sobolev exponents, J. Differ. Equ. 93 (1991), 283–310. Google Scholar

[10] 10.Zou, H., On the effect of domain geometry on uniqueness of positive solutions of Δ u+u p=0, Ann. Scuola Norm. Super. Pisa 21 (1994), 343–356. Google Scholar

[11] 11.Zou, H., A priori estimates for semilinear elliptic system without variational structure and their application, Math. Ann. 323 (2002), 713–735. Google Scholar | DOI

[12] 12.de Figueiredo, D. and Felmer, P., A Liouville type theorem for systems, Ann. Scuola Norm. Super. Pisa 21 (1994), 387–397. Google Scholar

[13] 13.Wei, J. C. and Zhang, L. Q., On the effect of the domain shape on the existence of large solutions of some superlinear problems, Preprint (2006). Google Scholar

[14] 14.Berestycki, H., Nirenberg, L. and Varadhan, S. N. S., The principle eigenvalues and maximum principle for second order elliptic operators in general domains, Commun. Pure Appl. Math. 47 (1994), 47–92. Google Scholar

[15] 15.Zhang, L. Q., Uniqueness of positive solutions of Δ u+u p=0 in a convex domain in R 2, Preprint (1992). Google Scholar

[16] 16.Zhang, L. Q., Uniqueness of positive solutions of Δ u+u+u p=0 in a finite ball, Commun. Part. Differ. Equ. 47 (1992), 1141–1164. Google Scholar

[17] 17.Lin, C. S., Uniqueness of solutions minimizing the functional ∫|∇ u|2/(∫|u|p+1)2/(p+1) in 2, Manuscript Math. 84 (1) (1994), 13–19. Google Scholar | DOI

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