×

On some singular periodic parabolic problems. (English) Zbl 1077.35008

The authors prove by the method of sub- and supersolutions the existence of positive periodic solutions to some singular parabolic problems on smooth bounded domains.

MSC:

35B10 Periodic solutions to PDEs
35K55 Nonlinear parabolic equations
35K20 Initial-boundary value problems for second-order parabolic equations
Full Text: DOI

References:

[1] Daners, D., Domain perturbation for linear and nonlinear parabolic equations, J. Differential Equations, 129, 358-402 (1996) · Zbl 0868.35059
[2] Daners, D., Periodic-parabolic eigenvalue problems with indefinite weight functions, Arch. Math., 68, 388-397 (1997) · Zbl 0874.35075
[3] D. Daners, P. Koch-Medina, Abstract evolution equations, periodic problems and applications, Longman Research Notes, vol. 279, 1992.; D. Daners, P. Koch-Medina, Abstract evolution equations, periodic problems and applications, Longman Research Notes, vol. 279, 1992. · Zbl 0789.35001
[4] J. Davila, M. Montenegro, Positive versus free boundary solutions to a singular equation, Preprint.; J. Davila, M. Montenegro, Positive versus free boundary solutions to a singular equation, Preprint. · Zbl 1173.35743
[5] Gilbarg, D.; Trudinger, N., Elliptic Partial Differential Equations of Second Order (1983), Springer: Springer Berlin · Zbl 0562.35001
[6] Godoy, T.; Kaufmann, U., On the existence of positive solutions for periodic parabolic sublinear problems, Abstr. Appl. Anal., 2003, 975-984 (2003) · Zbl 1133.35380
[7] Godoy, T.; Lami Dozo, E.; Paczka, S., The periodic parabolic eigenvalue problem with \(L^\infty\) weight, Math. Scand., 81, 20-34 (1997) · Zbl 0892.35071
[8] Hernández, J.; Mancebo, F.; Vega, J., On the linearization of some singular, nonlinear elliptic problems and applications, Ann. Inst. Henri Poincare, Anal. Non Lineaire, 19, 777-813 (2002) · Zbl 1020.35065
[9] J. Hernández, F. Mancebo, J. Vega, Positive solutions for singular nonlinear elliptic equations, Preprint.; J. Hernández, F. Mancebo, J. Vega, Positive solutions for singular nonlinear elliptic equations, Preprint. · Zbl 1180.35231
[10] O. Ladysženkaja, V. Solonnikov, N. Ural’ceva, Linear and quasilinear equations of parabolic type, Translation of Mathematical Monographs, vol 23, American Mathematical Society, 1968.; O. Ladysženkaja, V. Solonnikov, N. Ural’ceva, Linear and quasilinear equations of parabolic type, Translation of Mathematical Monographs, vol 23, American Mathematical Society, 1968. · Zbl 0174.15403
[11] Lieberman, G., Time-periodic solutions of linear parabolic differential equations, Comm. Partial Differential Equations, 24, 631-664 (1999) · Zbl 0928.35012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.