Existence results and a priori estimates for solutions of quasilinear problems with gradient terms
In this paper we establish a priori estimates and then an existence theorem of positive solutions for a Dirichlet problem on a bounded smooth domain in \(\mathbb{R}^N\) with a nonlinearity involving gradient terms. The existence result is proved with no use of a Liouville theorem for the limit probl...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
AGH Univeristy of Science and Technology Press
2019-01-01
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| Series: | Opuscula Mathematica |
| Subjects: | |
| Online Access: | https://www.opuscula.agh.edu.pl/vol39/2/art/opuscula_math_3913.pdf |
| Summary: | In this paper we establish a priori estimates and then an existence theorem of positive solutions for a Dirichlet problem on a bounded smooth domain in \(\mathbb{R}^N\) with a nonlinearity involving gradient terms. The existence result is proved with no use of a Liouville theorem for the limit problem obtained via the usual blow up method, in particular we refer to the modified version by Ruiz. In particular our existence theorem extends a result by Lorca and Ubilla in two directions, namely by considering a nonlinearity which includes in the
gradient term a power of \(u\) and by removing the growth condition for the nonlinearity \(f\) at \(u=0\). |
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| ISSN: | 1232-9274 |