×

On the radial solutions of a degenerate quasilinear elliptic equation in \(\mathbb{R}^N\). (English) Zbl 0959.35070

The paper is devoted to the study of a quasilinear elliptic equation in \(\mathbb{R}^N\) with the \(p\)-Laplacian as principal part. The existence, uniqueness and qualitative behavior of radially-symmetric solutions are investigated.

MSC:

35J70 Degenerate elliptic equations
35J60 Nonlinear elliptic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B99 Qualitative properties of solutions to partial differential equations
PDFBibTeX XMLCite
Full Text: DOI Numdam EuDML

References:

[1] Diaz, J.I. and Saa, J.E. - Uniqueness of very singular self-similar solution of a quasilinear degenerate parabolic equation with absorption, Publicacions Matemàtiques, Vol. 36 (1992), 19-38. · Zbl 0794.35091
[2] Gmira, A. - On quasilinear parabolic equation involving measure data, Asymptotic Analysis3 (1990), 43-56. · Zbl 0733.35017
[3] Guedda, M. and Veron, L. - Local and global properties of solutions of quasilinear elliptic equation, J. Diff. Eq.76, n° 1 (1988), 159-189. · Zbl 0661.35029
[4] Haraux, A. and Weissler, F.B. - Non uniqueness for a semilinear initial value problem, Indiana Univ. Math. J., 31 (1982), 167-189. · Zbl 0465.35049
[5] Kamin, S. and Vazquez, J.L. - Singular solutions of some nonlinear parabolic equations, J. d’Analyse Mathematique, Vol. 59 (1992), 51-74. · Zbl 0802.35066
[6] Naito, Y. and Yashida, K. - Damped oxillation of solutions for some nonlinear second order ordinary differential equation, Adv. in Math. Sciences and App., Gakkotosho, Tokyo, vol. 5, n° 1 (1995), 239-248. · Zbl 0829.34027
[7] Peletier, L.A., Terman, D. and Weissler, F.B. - On the equation Δu + 1/2 x∇u + f(u) = 0, Arch. Rational Mech. Anal., 94 (1986), 83-99. · Zbl 0615.35034
[8] Peletier, L.A. and Wang, J. - A very singular solution of a quasilinear degenerate diffusion equation with absorption, Trans. Am. Math. Soc., 307 (1988), 813-826. · Zbl 0696.35094
[9] Pucci, P., Serrin, J. - Continuation and limit properties for solutions of strongly non linear second order differential equations, Asymptotic Analysis, 4 (1991), 97-160. North-Holland. · Zbl 0733.34042
[10] Weissler, F.B. - Asymptotic Analysis of an ordinary differential equation and non-uniqueness for a semilinear partial differential equation, Archive for Rational Mech and Anal.91 (1986), 231-245. · Zbl 0614.35043
[11] Yoshida, K. - “Functional Analysis”, Grundlehren der mathematischen Wissens chaften123. Springer-Verlag, New York. Sixth edition (1980). · Zbl 0435.46002
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.