Uniqueness of ground states for quasilinear elliptic equations

Indiana University Mathematics Journal

Volumn 49, Issue 3, 2000, Pages 897-923

  Serrin, James ^a   Tang, Moxun ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Quasilinear elliptic equations; Scalar field equation

Indexed keywords

EID: 0000820023     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.2000.49.1893     Document Type: Article

References (30)

1. D. ANDERSON & G. DERRICK, Stability of time dependent particle like solutions in nonlinear field theories, J. Math. Phys. 11 (1970), 1336-1346.
2. D. ANDERSON & G. DERRICK, Stability of time dependent particle like solutions in nonlinear field theories, J. Math. Phys. 12 (1971), 945-952.
3. H. BERESTYCKI & P.-L. LIONS, Non-linear scalar field equations. I, Existence of a ground state, II, Existence of infinitely many solutions, Arch. Rational Mech. Anal. 82 (1983), 313-375.
4. n, n ≥ 3, Comm. Partial Diff. Eqs. 16 (1991), 1549-1572.
5. pu + f (u) = 0, Boll. Un. Mat. Ital. B 7 (1993), 283-310.
6. 3 = 0 and a variational characterization of other solutions, Arch. Rational Mech. Anal. 46 (1972), 81-95.
7. N with a non-Lipschitzian non-linearity, Advances in Diff. Eqs. 1 (1996), 199-218.
8. N, N ≥ 3, Arch. Rational Mech. Anal. 142 (1998), 127-141.
9. L. ERBE & M. TANG, Uniqueness theoremsfor positive solutions of quasilinear elliptic equations in a ball, J. Diff. Eqs. 138 (1997), 351-379.
10. n, Advances in Math. 118 (1996), 177-243.
11. M. GARCA-HUIDOBRO, R. MANSEVICH, J. SERRIN, M. TANG & C. YARUR, Ground states and free boundary value problems for the n-Laplacian in n dimensional space, J. Funct. Anal 172 (2000), 177-201.
12. F. GAZZOLA, J. SERRIN & M. TANG, Existence of ground states and free boundary problems for quasilinear elliptic operators, Advances in Diff. Eqs 5 (2000), 1-30.
13. B. GIDAS, W.M. NI & L. NIRENBERG, Symmetry of positive solutions of nonlinear elliptic equations in ℝn, Adv. in Math. Suppl. Stud. 7a (1981), 369-402.
14. n, Arch. Rational Mech. Anal. 105 (1989), 243-266.
15. M.K. KWONG & L. ZHANG, Uniqueness of the positive solution of Δu + f(u) = 0 in an annulus, Diff. Int. Eqs. 4 (1991), 583-596.
16. n, II, Tran. Amer. Math. Soc. 339 (1993), 495-505.
17. n, Arch. Rational Mech. Anal. 99 (1987), 115-145.
18. W.-M. NI & J. SERRIN, Nonexistence theorems for quasilinear partial differential equations, Rend. Circolo Mat. Palermo (Centenary Supplement) 8 (1985), 171-185.
19. _, Existence and nonexistence theorems for ground states for quasilinear partial differential equations. The anomalous case, Rome, Accad. Naz. dei Lincei, Atti dei Connegni 77 (1986), 231-257.
20. N, Arch. Rational Mech. Anal. 81 (1983), 181-197.
21. N, J. Diff. Eqs. 61 (1986), 380-397.
22. P. PUCCI & J. SERRIN, A general variational identity, Indiana Univ. Math. J. 35 (1986), 681-703.
23. _, Uniqueness of ground states for quasilinear elliptic operators, Indiana Univ. Math. J. 47 (1998), 501-528.
24. _, Uniqueness of ground states for quasilinear elliptic equations in the exponential case, Indiana Univ. Math. J. 47 (1998), 529-539.
25. J. SERRIN & H. ZOU, Symmetry of ground states of quasilinear elliptic equations, Arch. Rational Mech. Anal 148 (1999), 265-290.
26. W. STRAUSS, Existence of solitary waves in higher dimensions, Comm. Math. Phys. 55 (1977), 149-162.
27. M. TANG, Existence and uniqueness of fast decay entire solutions of quasilinear elliptic equations, J. Diff. Eqs 164 (2000), 155-179.
28. _, Uniqueness and global structure of positive radial solutions for quasilinear elliptic equations, Comm. Partial Diff. Eqs. (to appear).
29. _, Uniqueness of positive radial solutions for n-Laplacian Dirichlet problems, to appear, Proc. Roy. Soc. Edinburgh Sect. A.
30. n, Arch. Rational Mech. Anal. 115 (1991), 257-274.