On stable solutions of quasilinear periodic-parabolic problems
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1987)
- Volume: 14, Issue: 1, page 123-141
- ISSN: 0391-173X
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topDancer, E. N., and Hess, P.. "On stable solutions of quasilinear periodic-parabolic problems." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 14.1 (1987): 123-141. <http://eudml.org/doc/83995>.
@article{Dancer1987,
author = {Dancer, E. N., Hess, P.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {sub- and supersolutions; nonlinear semigroup; stable stationary solution; existence; stable T-periodic solutions; quasilinear second order parabolic equation},
language = {eng},
number = {1},
pages = {123-141},
publisher = {Scuola normale superiore},
title = {On stable solutions of quasilinear periodic-parabolic problems},
url = {http://eudml.org/doc/83995},
volume = {14},
year = {1987},
}
TY - JOUR
AU - Dancer, E. N.
AU - Hess, P.
TI - On stable solutions of quasilinear periodic-parabolic problems
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1987
PB - Scuola normale superiore
VL - 14
IS - 1
SP - 123
EP - 141
LA - eng
KW - sub- and supersolutions; nonlinear semigroup; stable stationary solution; existence; stable T-periodic solutions; quasilinear second order parabolic equation
UR - http://eudml.org/doc/83995
ER -
References
top- [1] H. Amann, Existence and multiplicity theorems for semilinear elliptic boundary value problems, Math. Z.150 (1976), pp. 281-295. Zbl0331.35026MR430526
- [2] H. Amann, Periodic solutions of semilinear parabolic equations, in Nonlinear Anal., eds. Cesari, Kannan and Weinberger, Academic Press, New York, 1978, pp. 1-29. Zbl0464.35050MR499089
- [3] A. Beltramo, P. Hess, On the principal eigenvalue of a periodic-parabolic operator, Comm. P.D.E.9 (1984), pp. 919-941. Zbl0563.35033MR749652
- [4] A. Castro A.C. Lazer, Results on periodic solutions of parabolic equations suggested by elliptic theory, Boll. Un. Mat. Ital. (6) I-B (1982), pp. 1089-1104. Zbl0501.35005MR683495
- [5] W.H. Fleming, A selection-migration model in population genetics, J. Math. Biol., 2 (1975), pp. 219-234. Zbl0325.92009MR403720
- [6] A. Friedman, Partial Differential Equations, Holt, Rinehart and Winston, 1969. Zbl0224.35002MR445088
- [7] D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math.840, Springer-Verlag, 1981. Zbl0456.35001MR610244
- [8] P. Hess, On positive solutions of semilinear-parabolic problems, in Lecture Notes in Math., Springer, 1076 (1984), pp. 101-114. Zbl0556.35066MR763357
- [9] P. Hess, Spatial homogeneity of stable solutions of some periodic-parabolic problems with Neumann boundary conditions, J. Differential Equations68 (1987), pp. 320-331. Zbl0619.35059MR891331
- [10] H. Hofer, Existence and multiplicity result for a class of second order elliptic equations, Proc. Roy. Soc. Edinburgh, 88A (1981), pp. 83-92. Zbl0468.35042MR611302
- [11] O.A. Ladyzenskaja, V.A. Solonnikov, N.N. Ural'ceva, Linear and quasilinear equations of parabolic type, Amer. Math. Soc. Transl. of Math. Monographs23, 1968. Zbl0174.15403MR241822
- [12] A.C. Lazer, Some remarks on periodic solutions of parabolic differential equations, in "Dynamical systems II", eds. Bednarek and Cesari, Academic Press, New York1982, pp. 227-346. Zbl0551.35044MR703697
- [13] H. Matano, Asymptotic behaviour and stability of solutions of semilinear diffusion equations, Publ. Res. Inst. Math. Sci., Kyoto Univ.15 (1979), pp. 401-454. Zbl0445.35063MR555661
- [14] H. Matano, Existence of nontrivial unstable sets for equilibriums of strongly order-preserving systems, J. Fac. Sci. Univ. Kyoto30 (1984), pp. 645-673. Zbl0545.35042MR731522
- [15] H. Matano, L∞ stability of an exponentially decreasing solution of the problem Δ u + f(x, u) = 0 in Rn, to appear in Japan J. Appl. Math. Zbl0594.35053
- [16] H. Matano, M. Mimura, Patterm formation in competition-diffusion systems in nonconvex domains, Publ. Res. Inst. Math. Sci., Kyoto Univ.19 (1983), pp. 1049-1079. Zbl0548.35063MR723460
- [17] M.H. Protter, H.F. Weinberger, Maximum principles in differential equations, Prentice-Hall, pp. 1967. Zbl0153.13602MR219861
- [18] D.H. Sattinger, Monotone methods in nonlinear elliptic and parabolic boundary value problems, Indiana Univ. Math. J.21 (1972), pp. 979-1000. Zbl0223.35038MR299921
- [19] J.C. Saut, B. Scheurer, Remarks on a nonlinear equation arising in population genetics, Comm. P.D.E.3 (1978), pp. 907-931. Zbl0421.35072MR507122
- [20] S. Senn, On a nonlinear elliptic eigenvalue problem with Neumann boundary conditions, with an application to population genetics, Comm. P.D.E.8 (1983), pp. 1199-1228. Zbl0526.35067MR709161
- [21] F.B. Weissler, Local existence and nonexistence for semilinear parabolic equations in Lp, Indiana Univ. Math. J.29 (1980), pp. 79-102. Zbl0443.35034MR554819
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