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We prove existence results of two solutions of the problem [ begin{cases} L(u)+u^{m-1}=lambda u^{p-1} & text{ in $Omega$}, quad u>0 &text{ in $Omega$}, quad u=0 & text{ on $partial Omega$}, end{cases} ] where $L(v)=-{rm div}(M(x) abla v)$ is a linear operator, $pin (2,2^{*}]$ and $lambda$ and $ m$ sufficiently large. Then their asymptotical limit as $mto +infty$ is investigated showing different behaviors.
Let $Omega subset mathbb{R}^N$ be a bounded domain and $delta(x)$ be the distance of a point $xin Omega$ to the boundary. We study the positive solutions of the problem $Delta u +frac{mu}{delta(x)^2}u=u^p$ in $Omega$, where $p>0, ,p e 1$ and $mu in m
This paper deals with existence and regularity of positive solutions of singular elliptic problems on a smooth bounded domain with Dirichlet boundary conditions involving the $Phi$-Laplacian operator. The proof of existence is based on a variant of t
We consider positive singular solutions to semilinear elliptic problems with possibly singular nonlinearity. We deduce symmetry and monotonicity properties of the solutions via the moving plane procedure.
We consider a sequence of blowup solutions of a two dimensional, second order elliptic equation with exponential nonlinearity and singular data. This equation has a rich background in physics and geometry. In a work of Bartolucci-Chen-Lin-Tarantello
This paper is concerned with the initial value problem for semilinear wave equation with structural damping $u_{tt}+(-Delta)^{sigma}u_t -Delta u =f(u)$, where $sigma in (0,frac{1}{2})$ and $f(u) sim |u|^p$ or $u |u|^{p-1}$ with $p> 1 + {2}/(n - 2 sig