Estimates on potential functions and boundary behavior of positive solutions for sublinear Dirichlet problems
We give global estimates on some potential of functions in a bounded domain of the Euclidean space ${\mathbb{R}}^n\; (n\geq 2)$. These functions may be singular near the boundary and are globally comparable to a product of a power of the distance to the boundary by some particularly well behaved...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2014-01-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2014/08/abstr.html |
| Summary: | We give global estimates on some potential of functions in a bounded domain
of the Euclidean space ${\mathbb{R}}^n\; (n\geq 2)$. These functions
may be singular near the boundary and are globally comparable to a product
of a power of the distance to the boundary by some particularly well behaved
slowly varying function near zero. Next, we prove the existence and uniqueness
of a positive solution for the integral equation $u=V(a u^{\sigma})$ with
$0\leq \sigma <1$, where V belongs to a class of kernels that contains
in particular the potential kernel of the classical Laplacian
$V=(-\Delta)^{-1}$ or the fractional laplacian
$V=(-\Delta)^{\alpha/2}$, $0<\alpha<2$. |
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| ISSN: | 1072-6691 |