Kodai Mathematical Journal

The Hadamard variational formula for the ground state value of $-\Delta u=łambda\vert u\vert^{p-1}u$

Tatsuzo Osawa

Full-text: Open access

Article information

Source
Kodai Math. J., Volume 15, Number 2 (1992), 258-278.

Dates
First available in Project Euclid: 23 January 2006

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1138039602

Digital Object Identifier
doi:10.2996/kmj/1138039602

Mathematical Reviews number (MathSciNet)
MR1185423

Zentralblatt MATH identifier
0825.35045

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35A15: Variational methods 35J20: Variational methods for second-order elliptic equations

Citation

Osawa, Tatsuzo. The Hadamard variational formula for the ground state value of $-\Delta u=łambda\vert u\vert^{p-1}u$. Kodai Math. J. 15 (1992), no. 2, 258--278. doi:10.2996/kmj/1138039602. https://projecteuclid.org/euclid.kmj/1138039602


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References

  • [1] R. ADAMS, Sobolev spaces, Academic Press (1975).
  • [2] S. AGMON, A. DOUGLIS AND L. NIRENBERG, Estimates near the boundary fo solutions of elliptic partial differential equations satisfying general boundary conditions I, Comm. pure Appl. Math., 12 (1959), 623-727.
  • [3] H. BREZIS AND L. NIRENBERG, Positive solutions of nonlinear elliptic equation involving critical Sobolev exponents, Commun. Pure and Appl. Math., 36 (1983), 437-477.
  • [4] E. N. DANCER, The effect of domain shape on the number of positive solution of certain nonlinear equations. J. of Diff. Equations., 74 (1988), 120-156.
  • [5] D. FUJIWARA AND S. OZAWA, Hadamard's variational formula for the Gree functions of some normal elliptic boundary problems, Proc. Japan Acad. 54A, (1978), 215-220.
  • [6] P. R. GARABEDIAN, Partial Differential Equations, J. Wiley and Sons. Inc., Ne York (1964).
  • [7] P. R. GARABEDIAN AND M. M. SCHIFFER, Convexity of domain functonals, J. Anal. Math. 2 (1978), 281-368
  • [8] B. GIDAS, W. M. Ni AND L. NIRENBERG, Symmetry and related properties via th maximum principle, Commun. Math. Phys., 68 (1979), 209-243.
  • [9] J. HADAMARD, Memoire sur le probleme d'anlyse relatif a equilibre des plaque elastiques encastrees, Oeuvres, C. N. R. S. torn 2 (1968), 515-631.
  • [10] S. OZAWA, Asymptotic property of an eigenfunction of the Laplacian unde singular variation of domains, --the Neumann conditions-- Osaka J. Math., 22 (1985), 639-655.
  • [11] T. OSAWA AND S. OZAWA, Nonlinear eigenvalue problems and singular variatio of domains (to appear in Kodai Math. J. ).