Stability for semilinear parabolic equations with decaying potentials in Rn and dynamical approach to the existence of ground states
Annales de l'I.H.P. Analyse non linéaire (2002)
- Volume: 19, Issue: 5, page 683-703
- ISSN: 0294-1449
Access Full Article
topHow to cite
topSouplet, Philippe, and Zhang, Qi S.. "Stability for semilinear parabolic equations with decaying potentials in Rn and dynamical approach to the existence of ground states." Annales de l'I.H.P. Analyse non linéaire 19.5 (2002): 683-703. <http://eudml.org/doc/78558>.
@article{Souplet2002,
author = {Souplet, Philippe, Zhang, Qi S.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {decaying potentials; elliptic equations; equilibria for parabolic equations},
language = {eng},
number = {5},
pages = {683-703},
publisher = {Elsevier},
title = {Stability for semilinear parabolic equations with decaying potentials in Rn and dynamical approach to the existence of ground states},
url = {http://eudml.org/doc/78558},
volume = {19},
year = {2002},
}
TY - JOUR
AU - Souplet, Philippe
AU - Zhang, Qi S.
TI - Stability for semilinear parabolic equations with decaying potentials in Rn and dynamical approach to the existence of ground states
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2002
PB - Elsevier
VL - 19
IS - 5
SP - 683
EP - 703
LA - eng
KW - decaying potentials; elliptic equations; equilibria for parabolic equations
UR - http://eudml.org/doc/78558
ER -
References
top- [1] Bahri A., Lions P.L., On the existence of a positive solution of semilinear elliptic equations in unbounded domains, Ann. Inst. Henri Poincaré, Anal. non linéaire14 (1997) 365-413. Zbl0883.35045MR1450954
- [2] Berestycki H., Capuzzo Dolcetta I., Nirenberg L., Superlinear indefinite elliptic problems and nonlinear Liouville theorems, Topol. Methods Nonlinear Anal.4 (1994) 59-78. Zbl0816.35030MR1321809
- [3] Berestycki H., Lions P.L., Nonlinear scalar field equations I, existence of a ground state, Arch. Rat. Mech. Anal.82 (1983) 313-346. Zbl0533.35029MR695535
- [4] Berestycki H., Lions P.L., Nonlinear scalar field equations II, existence of infinitely many solutions, Arch. Rat. Mech. Anal.82 (1983) 347-376. Zbl0556.35046MR695536
- [5] Cazenave T., Lions P.L., Solutions globales d'équations de la chaleur semilinéaires, Comm. Partial Differential Equations9 (1984) 955-978. Zbl0555.35067MR755928
- [6] Cazenave T., Weissler F.B., Asymptotically self-similar global solutions of the nonlinear Schrödinger and heat equations, Math. Z.228 (1998) 83-120. Zbl0916.35109MR1617975
- [7] Deng K., Levine H.A., The role of critical exponents in blowup theorems, the sequel, J. Math. Anal. Appl.243 (2000) 85-126. Zbl0942.35025MR1742850
- [8] Ding W.Y., Ni W.M., On the existence of positive entire solutions of a semilinear elliptic equation, Arch. Rat. Mech. Anal.91 (1986) 283-308. Zbl0616.35029MR807816
- [9] Feireisl E., Petzeltova H., Convergence to a ground state as a threshold phenomenon in nonlinear parabolic equations, Differential Integral Equations10 (1997) 181-196. Zbl0879.35023MR1424805
- [10] Fila M., Souplet Ph., Weissler F.B., Linear and nonlinear heat equations in Lqδ spaces and universal bounds for global solutions, Math. Annalen320 (2001) 87-113. Zbl0993.35023
- [11] Fujita H., On the blowing up of solutions of the Cauchy problem for ut=Δu+u1+α, J. Fac. Sci. Univ. Tokyo Sect. I13 (1966) 109-124. Zbl0163.34002
- [12] Gidas B., Spruck J., Global and local behaviour of positive solutions of nonlinear elliptic equations, Comm. Pure Appl. Math.34 (1981) 525-598. Zbl0465.35003MR615628
- [13] Giga Y., A bound for global solutions of semilinear heat equations, Comm. Math. Phys.103 (1986) 415-421. Zbl0595.35057MR832917
- [14] Haraux A., Weissler F.B., Non-uniqueness for a semilinear initial value problem, Indiana Univ. Math. J.31 (1982) 167-189. Zbl0465.35049MR648169
- [15] Kato T., Strong Lp-solutions of the Navier–Stokes equation in Rm, with applications to weak solutions, Math. Z.187 (1984) 471-480. Zbl0545.35073MR760047
- [16] Kuzin I., Pohozaev S., Entire Solutions of Semilinear Elliptic Equations, Birkhäuser, 1997. Zbl0882.35003MR1479168
- [17] Levine H.A., Some nonexistence and instability theorems for solutions of formally parabolic equations of the form Put=−Au+F(u), Arch. Rat. Mech. Anal.51 (1973) 371-386. Zbl0278.35052
- [18] Levine H.A., The role of critical exponents in blow up theorems, SIAM Rev.32 (1990) 262-288. Zbl0706.35008MR1056055
- [19] Lieberman G., Second Order Parabolic Differential Equations, World Scientific, Singapore, 1996. Zbl0884.35001MR1465184
- [20] Lions P.L., The concentration compactness principle in the calculus of variation. The locally compact case, part I, II, Ann. Inst. Henri Poincaré, Anal. non linéaire1 (1984) 109-145, 223–283. Zbl0704.49004
- [21] Moser J., A Harnack inequality for parabolic differential equations, Comm. Pure Appl. Math.17 (1964) 101-134. Zbl0149.06902MR159139
- [22] Murata M., Structure of positive solutions to (−Δ+V)u=0 in Rm, Duke Math. J.53 (1986) 869-943. Zbl0624.35023
- [23] Ni W.M., Sacks P., Tavantzis J., On the asymptotic behavior of solutions of certain quasilinear parabolic equations, J. Differential Equations54 (1984) 97-120. Zbl0565.35053MR756548
- [24] Noussair E., Swanson C.A., Existence theorems for generalized Klein Gordon equations, Bull. Amer. Math. Soc.31 (1983) 333-336. Zbl0524.35048MR684902
- [25] Quittner P., Universal bound for global positive solutions of a superlinear parabolic problem, Math. Annalen320 (2001) 299-305. Zbl0981.35010MR1839765
- [26] Souplet Ph., Sur l'asymptotique des solutions globales pour une équation de la chaleur semi-linéaire dans des domaines non bornés, C. R. Acad. Sci. Paris323 (1996) 877-882. Zbl0860.35051MR1414551
- [27] Souplet Ph., Geometry of unbounded domains, Poincaré inequalities and stability in semilinear parabolic equations, Comm. Partial Differential Equations24 (1999) 951-973. Zbl0926.35064MR1680893
- [28] Souplet Ph., Zhang Q.S., Existence of ground states for semilinear elliptic equations with decaying mass: a parabolic approach, C. R. Acad. Sci. Paris332 (2001) 515-520. Zbl0992.35029MR1834061
- [29] Weissler F.B., Semilinear evolution equations in Banach spaces, J. Funct. Anal.32 (1979) 277-296. Zbl0419.47031MR538855
- [30] Weissler F.B., Local existence and nonexistence for semilinear parabolic equations in Lp, Indiana Univ. Math. J.29 (1980) 79-102. Zbl0443.35034MR554819
- [31] Weissler F.B., Existence and nonexistence of global solutions for a semilinear heat equation, Israel J. Math.38 (1981) 29-40. Zbl0476.35043MR599472
- [32] Zhang Q.S., Large time behavior of Schrödinger heat kernels and applications, Comm. Math. Phys.210 (2000) 371-398. Zbl0978.35014MR1776837
- [33] Zhang Q.S., Semilinear parabolic equations on manifolds and applications to the non-compact Yamabe problem, Electron. J. Differential Equations46 (2000) 1-30. Zbl0984.58011MR1764702
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.