A generalized Pohozaev identity and its applications

Nichiro KAWANO; Wei-Ming NI; Shoji YOTSUTANI

doi:10.2969/jmsj/04230541

Nichiro KAWANO, Wei-Ming NI, Shoji YOTSUTANI

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JOURNAL FREE ACCESS

1990 Volume 42 Issue 3 Pages 541-564

DOI https://doi.org/10.2969/jmsj/04230541

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Published: 1990 Received: September 01, 1988 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) H. Berestycki and P. L. Lions, Nonlinear scalar field equations, I. Existence of ground states, Arch. Rational Mech. Anal., 82 (1983), 313-345.
2) W.-Y. Ding and W.-M. Ni, On the elliptic equation Δu+Ku^(n+2)/(n-2)=0 and related topics, Duke Math. J., 52 (1985), 486-506.
3) T. Kusano and M. Naito, Oscillation theory of entire solutions of second order superlinear elliptic equations, Funckcial. Ekvac., 30 (1987), 269-282.
4) N. Kawano, J. Satsuma and S. Yotsutani, Existence of positive entire solutions of an Emden-type elliptic equation, Funckcial. Ekvac., 31 (1988), 121-145.
5) Z. Nehari, On a class of nonlinear second-order differential equations, Trans. Amer. Math. Soc., 95 (1960), 101-123.
6) W.-M. Ni, On the elliptic equation Δu+K(x)u^(n+2)/(n-2)=0 its generalization, and applications in geometry, Indiana Univ. Math. J., 31 (1982), 493-529.
7) W.-M. Ni, Uniqueness, nonuniqueness and related questions of nonlinear elliptic and parabolic equations, Proc. Sympos. Pure Math., 45 (1986), 229-241.
8) W.-M. Ni, Some Aspects of Semilinear Elliptic Equations, Lecture Note, National Tsing Hua University, Taiwan, 1987.
9) W.-M. Ni and J. Serrin, Non-existence theorems for quasilinear partial differential equations, Rend. Circ. Mat. Palermo, Suppl., 8 (1985), 171-185.
10) W.-M. Ni and J. Serrin, Existence and non-existence theorems for ground states for quasilinear partial differential equations, Atti Convegni Lincei, 77 (1985), 231-257.
11) W.-M. Ni and J. Serrin, Nonexistence theorems for singular solutions of quasilinear partial differential equations, Comm. Pure Appl. Math., 39 (1986), 379-399.
12) W.-M. Ni and S. Yotsutani, On the Matukuma's equation and related topics, Proc. Japan Acad. Ser. A, 62 (1986), 260-263.
13) W.-M. Ni and S. Yotsutani, Semilinear elliptic equations of Matukuma-type and related topics, Japan J. Appl. Math., 5 (1988), 1-32.
14) M. Otani, Existence and nonexistence of nontrivial solutions of some nonlinear degenerate elliptic equations, J. Funct. Anal., 76 (1988), 140-159.
15) S. I. Pohozaev, Eigenfunctions of the equations Δu+λf(u)=0, Soviet Math. Dokl., 5 (1965), 1408-1411.
16) P. Pucci and J. Serrin, A general variational identity, Indiana Univ. Math. J., 35 (1986), 682-703.
17) H. Rellich, Darstellung der eigenwerte von Δu+λu=0 darch ein randintegral, Math. Z., 46 (1940), 635-636.

Right : [1] H. Berestycki and P. L. Lions, Nonlinear scalar field equations, I. Existence of ground states, Arch. Rational Mech. Anal., 82 (1983), 313-345.
[2] W. -Y. Ding and W. -M. Ni, On the elliptic equation Δu+Ku^(n+2)/(n-2)=0 and related topics, Duke Math. J., 52 (1985), 486-506.
[3] T. Kusano and M. Naito, Oscillation theory of entire solutions of second order superlinear elliptic equations, Funckcial. Ekvac., 30 (1987), 269-282.
[4] N. Kawano, J. Satsuma and S. Yotsutani, Existence of positive entire solutions of an Emden-type elliptic equation, Funckcial. Ekvac., 31 (1988), 121-145.
[5] Z. Nehari, On a class of nonlinear second-order differential equations, Trans. Amer. Math. Soc., 95 (1960), 101-123.
[6] W. -M. Ni, On the elliptic equation Δu+K(x)u^(n+2)/(n-2)=0 its generalization, and applications in geometry, Indiana Univ. Math. J., 31 (1982), 493-529.
[7] W. -M. Ni, Uniqueness, nonuniqueness and related questions of nonlinear elliptic and parabolic equations, Proc. Sympos. Pure Math., 45 (1986), 229-241.
[8] W. -M. Ni, Some Aspects of Semilinear Elliptic Equations, Lecture Note, National Tsing Hua University, Taiwan, 1987.
[9] W. -M. Ni and J. Serrin, Non-existence theorems for quasilinear partial differential equations, Rend. Circ. Mat. Palermo, Suppl., 8 (1985), 171-185.
[10] W. -M. Ni and J. Serrin, Existence and non-existence theorems for ground states for quasilinear partial differential equations, Atti Convegni Lincei, 77 (1985), 231-257.
[11] W. -M. Ni and J. Serrin, Nonexistence theorems for singular solutions of quasilinear partial differential equations, Comm. Pure Appl. Math., 39 (1986), 379-399.
[12] W. -M. Ni and S. Yotsutani, On the Matukuma's equation and related topics, Proc. Japan Acad. Ser. A, 62 (1986), 260-263.
[13] W. -M. Ni and S. Yotsutani, Semilinear elliptic equations of Matukuma-type and related topics, Japan J. Appl. Math., 5 (1988), 1-32.
[14] M. Ôtani, Existence and nonexistence of nontrivial solutions of some nonlinear degenerate elliptic equations, J. Funct. Anal., 76 (1988), 140-159.
[15] S. I. Pohozaev, Eigenfunctions of the equations Δu+λf(u)=0, Soviet Math. Dokl., 5 (1965), 1408-1411.
[16] P. Pucci and J. Serrin, A general variational identity, Indiana Univ. Math. J., 35 (1986), 682-703.
[17] H. Rellich, Darstellung der eigenwerte von Δu+λu=0 darch ein randintegral, Math. Z., 46 (1940), 635-636.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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