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This paper is concerned with the existence, uniqueness and asymptotic behavior of classical solutions to two classes of models-   △  ⁢  u    ±   λ  ⁢|   ∇  ⁡  u   |   2    u  β=   b  ⁢   (  x  )   ⁢   u   -  α{-\triangle u\pm\lambda\frac{|\nabla u|^{2}}{u^{\beta}}=b(x)u^{-\alpha}}   ,u  &gt;  0{u&gt;0}   ,x  ∈  Ω{x\in\Omega}   ,u  |    ∂  ⁡  Ω    =  0{u|_{\partial\Omega}=0}   , where Ω is a bounded domain with smooth boundary inℝ  N{\mathbb{R}^{N}}   ,λ  &gt;  0{\lambda&gt;0}   ,β  &gt;  0{\beta&gt;0}   ,α  &gt;   -  1{\alpha&gt;-1}   , andb  ∈    C  loc  ν   ⁢   (  Ω  ){b\in C^{\nu}_{\mathrm{loc}}(\Omega)}    for someν  ∈   (  0  ,  1  ){\nu\in(0,1)}   , and  b  is positive in Ω but may be vanishing or singular on∂  ⁡  Ω{\partial\Omega}   . Our approach is largely based on nonlinear transformations and the construction of suitable sub- and super-solutions.

Two Classes of Nonlinear Singular Dirichlet Problems with Natural Growth: Existence and Asymptotic Behavior