Existence of regular and singular bound state solutions to a quasilinear equation
Abstract The existence of regular and singular bound state solutions to △ p u + f ( u ) = 0 , r ∈ R n ∖ { 0 } $$ \triangle _{p}u+f(u)=0,~~~r\in \mathbb{R}^{n}\backslash \{0\} $$ is considered. Our result concerns the solution according to its behavior as r → 0 $r\rightarrow 0$ and r → ∞ $r\rightarro...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-07-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-025-02092-w |
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| Summary: | Abstract The existence of regular and singular bound state solutions to △ p u + f ( u ) = 0 , r ∈ R n ∖ { 0 } $$ \triangle _{p}u+f(u)=0,~~~r\in \mathbb{R}^{n}\backslash \{0\} $$ is considered. Our result concerns the solution according to its behavior as r → 0 $r\rightarrow 0$ and r → ∞ $r\rightarrow \infty $ . Under the assumption that f is supercritical for small u > 0 $u>0$ and is subcritical for large u > 0 $u>0$ , we show the existence of various types of solutions. The Pohozaev identity plays a crucial role in our investigation. |
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| ISSN: | 1687-2770 |