Existence of minimal solutions to quasilinear elliptic equations with several sub-natural growth terms
| Autor: | Hara, Takanobu, Seesanea, Adisak |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.na.2020.111847 |
| Popis: | We study the existence of positive solutions to quasilinear elliptic equations of the type \[ -\Delta_{p} u = \sigma u^{q} + \mu \quad \text{in} \ \mathbb{R}^{n}, \] in the sub-natural growth case $0 < q < p - 1$, where $\Delta_{p}u = \nabla \cdot ( |\nabla u|^{p - 2} \nabla u )$ is the $p$-Laplacian with $1 < p < n$, and $\sigma$ and $\mu$ are nonnegative Radon measures on $\mathbb{R}^{n}$. We construct minimal generalized solutions under certain generalized energy conditions on $\sigma$ and $\mu$. To prove this, we give new estimates for interaction between measures. We also construct solutions to equations with several sub-natural growth terms using the same methods. Comment: Published online in Nonlinear Analysis |
| Databáze: | arXiv |
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