Large and entire large solution for a quasilinear problem

Abstract In this article we give the existence results for the quasilinear elliptic problem Δ p u = b ( x ) f ( u ) in Ω , u ( x ) → ∞ as x → ∂ Ω , where Ω ⊆ R N is a domain.

[1]  J. Díaz,et al.  Existence et unicité de solutions positives pour certaines équations elliptiques quasilinéaires , 1987 .

[2]  P. Tolksdorf,et al.  Regularity for a more general class of quasilinear elliptic equations , 1984 .

[3]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[4]  V. Kondratiev,et al.  Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains , 2006 .

[5]  Emmanuele DiBenedetto,et al.  C1 + α local regularity of weak solutions of degenerate elliptic equations , 1983 .

[6]  Zhijun Zhang,et al.  A remark on the existence of explosive solutions for a class of semilinear elliptic equations , 2000 .

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

[8]  Shuangping Tao,et al.  On the existence of explosive solutions for semilinear elliptic problems , 2002 .

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

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

[11]  Alan V. Lair,et al.  A Necessary and Sufficient Condition for Existence of Large Solutions to Semilinear Elliptic Equations , 1999 .

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

[13]  Ahmed Mohammed,et al.  Existence and asymptotic behavior of blow-up solutions to weighted quasilinear equations , 2004 .

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

[15]  Zongming Guo,et al.  Uniqueness of positive solutions for quasilinear elliptic equations when a parameter is large , 1994, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.