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In this paper, for more general  f ,  g  and  a ,  b , we obtain conditions about the existence and boundary behavior of solutions to boundary blow-up elliptic problems▵  u  =  a   (  x  )   g   (  u  )   +    b   (  x  )   f   (  u  )   |  ∇  u  |   q,    x  ∈  Ω  ,    u  |    ∂  Ω    =  +  ∞    $ \triangle u=a(x)g(u)+ b(x) f(u)|\nabla u|^q,\quad x\in \Omega ,\quad u|_{\partial \Omega }=+\infty $    and improve and generalize most of the previously available results in the literature, where Ω is a bounded domain with smooth boundary in ℝ  N  ,q  ∈  (  0  ,  2  ]    ${q\in (0, 2]}$   ,a  ,  b  ∈   C  ν    (   Ω  ¯   )${a, b \in C^{\nu }(\overline{\Omega })}$    which are positive in Ω, may be vanishing on the boundary, andf  ,  g  ∈  C   [  0  ,  ∞  )   ∩   C  1    (  0  ,  ∞  )${f, g\in C[0, \infty ) \cap C^1(0, \infty ) }$    orf  ,  g  ∈   C  1    (  ℝ  )${f, g\in C^1(\mathbb {R}) }$   , which are increasing.

The existence and boundary behavior of large solutions to semilinear elliptic equations with nonlinear gradient terms