Regularizing effect of absorption terms in singular problems

@article{Oliva2019RegularizingEO,
  title={Regularizing effect of absorption terms in singular problems},
  author={Francescantonio Oliva},
  journal={Journal of Mathematical Analysis and Applications},
  year={2019}
}
  • Francescantonio Oliva
  • Published 31 October 2018
  • Mathematics
  • Journal of Mathematical Analysis and Applications
We prove existence of solutions to problems whose model is $$\begin{cases} \displaystyle -\Delta_p u + u^q = \frac{f}{u^\gamma} & \text{in}\ \Omega, \newline u\ge0 &\text{in}\ \Omega,\newline u=0 &\text{on}\ \partial\Omega, \end{cases}$$ where $\Omega$ is an open bounded subset of $\mathbb{R}^N$ ($N\ge2$), $\Delta_p u$ is the $p$-laplacian operator for $1\le p 0$, $\gamma\ge 0$ and $f$ is a nonnegative function in $L^m(\Omega)$ for some $m\ge1$. In particular we analyze the regularizing… 
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References

SHOWING 1-10 OF 59 REFERENCES
On Dirichlet problems with singular nonlinearity of indefinite sign
Let $\Omega$ be a smooth bounded domain in $\mathbb{R}^{N}$, $N\geq1$, let $K$, $M$ be two nonnegative functions and let $\alpha,\gamma>0$. We study existence and nonexistence of positive solutions
The Dirichlet problem for singular elliptic equations with general nonlinearities
In this paper, under very general assumptions, we prove existence and regularity of distributional solutions to homogeneous Dirichlet problems of the form $$\begin{aligned} {\left\{ \begin{array}{ll}
The role of the power 3 for elliptic equations with negative exponents
Let $$\Omega \subset {\mathbb{R }}^{N}$$ be a bounded regular domain of dimension $$N\ge 3,\;h$$ a positive $$L^{1}$$ function on $$\Omega .$$ Elliptic equations of singular growth like
On the behaviour of the solutions to p-Laplacian equations as p goes to 1
In the present paper we study the behaviour as $p$ goes to $1$ of the weak solutions to the problems $$ \begin{cases} -\operatorname{div} \bigl(|\nabla u_p|^{p-2}\nabla u_p\bigr)=f &\text{in }
On a Dirichlet problem in bounded domains with singular nonlinearity
In this paper we prove the existence and regularity of positive solutions of the homogeneous Dirichlet problem \begin{equation*} -Δ u=g(x,u) in   \Omega, u=0  on ∂ \Omega, \end{equation*} where
Existence and uniqueness results for possibly singular nonlinear elliptic equations with measure data
We study existence and uniqueness of solutions to a nonlinear elliptic boundary value problem with a general, and possibly singular, lower order term, whose model is $$\begin{aligned} {\left\{
A Lazer-McKenna type problem with measures
In this paper we are concerned with a general singular Dirichlet boundary value problem whose model is the following $$ \begin{cases} -\Delta u = \frac{\mu}{u^{\gamma}} & \text{in}\ \Omega, u=0
An Overview on Singular Nonlinear Elliptic Boundary Value Problems
We give a survey of old and recent results concerning existence and multiplicity of positive solutions (classical or weak) to nonlinear elliptic equations with singular nonlinear terms of the form
A semilinear elliptic equation with a mild singularity at $u=0$: existence and homogenization
In this paper we consider semilinear elliptic equations with singularities, whose prototype is the following \begin{equation*} \begin{cases} \displaystyle - div \,A(x) D u = f(x)g(u)+l(x)& \mbox{in}
Definition, existence, stability and uniqueness of the solution to a semilinear elliptic problem with a strong singularity at u = 0
In this paper we consider a semilinear elliptic equation with a strong singularity at $u=0$, namely \displaystyle u\geq 0 & \mbox{in } \Omega, \displaystyle - div \,A(x) D u = F(x,u)& \mbox{in} \;
...
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