Existence and blow-up rate of large solutions of p(x)-Laplacian equations with gradient terms
| Autor: | Haitao Wu, Jingjing Liu, Qihu Zhang, Patrizia Pucci |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
p(x) Laplacian
Pointwise Applied Mathematics 010102 general mathematics Mathematical analysis singularity 01 natural sciences 010101 applied mathematics supersolution Singularity Monotone polygon subsolution boundary blow-up solution 0101 mathematics p(x) Laplacian subsolution supersolution boundary blow-up solution singularity Laplace operator Analysis Mathematical physics Mathematics |
| Zdroj: | Journal of Mathematical Analysis and Applications. 457:944-977 |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2017.08.038 |
| Popis: | In this paper we investigate boundary blow-up solutions of the problem { − Δ p ( x ) u + f ( x , u ) = ± K ( x ) | ∇ u | m ( x ) in Ω , u ( x ) → + ∞ as d ( x , ∂ Ω ) → 0 , where Δ p ( x ) u = div ( | ∇ u | p ( x ) − 2 ∇ u ) is called the p ( x ) -Laplacian. Our results extend the previous work [25] of Y. Liang, Q.H. Zhang and C.S. Zhao from the radial case to the non-radial setting, and [46] due to Q.H. Zhang and D. Motreanu from the assumption that K ( x ) | ∇ u ( x ) | m ( x ) is a small perturbation, to the case in which ± K ( x ) | ∇ u | m ( x ) is a large perturbation. We provide an exact estimate of the pointwise different behavior of the solutions near the boundary in terms of d ( x , ∂ Ω ) and in terms of the growth of the exponents. Furthermore, the comparison principle is no longer applicable in our context, since f ( x , ⋅ ) is not assumed to be monotone in this paper. |
| Databáze: | OpenAIRE |
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