Boundary blow-up in nonlinear elliptic equations of Bieberbach–Rademacher type

The research of the first author was carried out at Victoria University (Melbourne) with the support of the Australian Government through DETYA. The second author has been supported by Grant 2-CEX06-11-18/2006.

[1]  Jorge García-Melián,et al.  Uniqueness and asymptotic behaviour for solutions of semilinear problems with boundary blow-up , 2001 .

[2]  P. Bassanini,et al.  Elliptic Partial Differential Equations of Second Order , 1997 .

[3]  E. N. Dancer,et al.  Asymptotic behavior of positive solutions of some elliptic problems , 2003 .

[4]  P. Fischer On the Inequality , 1974, Canadian Mathematical Bulletin.

[5]  E. Dynkin Diffusions, Superdiffusions and Partial Differential Equations , 2002 .

[6]  E. B. Dynkin,et al.  A probabilistic approach to one class of nonlinear differential equations , 1991 .

[7]  G. Temple Partial Differential Equations of Elliptic Type , 1971 .

[8]  S. Resnick Extreme Values, Regular Variation, and Point Processes , 1987 .

[9]  Catherine Bandle,et al.  Asymptotic behaviour of large solutions of quasilinear elliptic problems , 2003 .

[10]  Alan C. Lazer,et al.  Asymptotic behavior of solutions of boundary blowup problems , 1994, Differential and Integral Equations.

[11]  Vicentiu D. Rădulescu,et al.  Extremal singular solutions for degenerate logistic-type equations in anisotropic media , 2004 .

[12]  Yihong Du,et al.  Positive solutions of an elliptic partial differential equation on RN , 2002 .

[13]  D. Gilbarg,et al.  Elliptic Partial Differential Equa-tions of Second Order , 1977 .

[14]  P. J. McKenna,et al.  On a problem of Bieberbach and Rademacher , 1993 .

[15]  M. Meerschaert Regular Variation in R k , 1988 .

[16]  E. Seneta Regularly varying functions , 1976 .

[17]  J. López-Gómez,et al.  Pointwise Growth and Uniqueness of Positive Solutions for a Class of Sublinear Elliptic Problems where Bifurcation from Infinity Occurs , 1998 .

[18]  L. Bieberbach Δu=eu und die automorphen Funktionen , 1916 .

[19]  J. Matero Quasilinear elliptic problems with boundary blow-up , 1995 .

[20]  Vicenţiu D. Rădulescu,et al.  EXISTENCE AND UNIQUENESS OF BLOW-UP SOLUTIONS FOR A CLASS OF LOGISTIC EQUATIONS , 2002 .

[21]  Robert Osserman,et al.  On the inequality $\Delta u\geq f(u)$. , 1957 .

[22]  J. Karamata,et al.  Sur un mode de croissance régulière. Théorèmes fondamentaux , 1933 .

[23]  Vicentiu D. R ˘ adulescu EXISTENCE AND UNIQUENESS OF BLOW-UP SOLUTIONS FOR A CLASS OF LOGISTIC EQUATIONS , 2002 .

[24]  Haim Brezis,et al.  Remarks on sublinear elliptic equations , 1986 .

[25]  L. Nirenberg,et al.  Partial Differential Equations Invariant under Conformal or Projective Transformations , 1974 .

[26]  S. Alama,et al.  On the solvability of a semilinear elliptic equation via an associated eigenvalue problem , 1996 .

[27]  J. Keller On solutions of δu=f(u) , 1957 .

[28]  J. Gall A Path-Valued Markov Process and its Connections with Partial Differential Equations , 1994 .

[29]  Yihong Du,et al.  Blow-Up Solutions for a Class of Semilinear Elliptic and Parabolic Equations , 1999, SIAM J. Math. Anal..

[30]  Florica-Corina St . Cand SOLUTIONS WITH BOUNDARY BLOW-UP FOR A CLASS OF NONLINEAR ELLIPTIC PROBLEMS , 2003 .

[31]  G. Talenti,et al.  Partial differential equations of elliptic type : Cortona, 1992 , 1994 .

[32]  Vicenţiu D. Rădulescu,et al.  Uniqueness of the blow-up boundary solution of logistic equations with absorbtion , 2002 .

[33]  E. N. Dancer Some remarks on classical problems and fine properties of Sobolev spaces , 1996, Differential and Integral Equations.