Nonlinear scalar field equation with competing nonlocal terms *
| Autor: | Pietro d'Avenia, Jarosław Mederski, Alessio Pomponio |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Mathematics::Commutative Algebra
Applied Mathematics Mathematics::Analysis of PDEs General Physics and Astronomy Statistical and Nonlinear Physics Omega 35J61 35B33 35B38 35Q55 35J20 Nonlinear system Mathematics - Analysis of PDEs FOS: Mathematics Beta (velocity) Scalar field Mathematical Physics Analysis of PDEs (math.AP) Mathematical physics Mathematics |
| Zdroj: | Nonlinearity. 34:5687-5707 |
| ISSN: | 1361-6544 0951-7715 |
| Popis: | We find radial and nonradial solutions to the following nonlocal problem $$-\Delta u +\omega u= \big(I_\alpha\ast F(u)\big)f(u)-\big(I_\beta\ast G(u)\big)g(u) \text{ in } \mathbb{R}^N$$ under general assumptions, in the spirit of Berestycki and Lions, imposed on $f$ and $g$, where $N\geq 3$, $0\leq \beta \leq \alpha0$, then we deal with two competing nonlocal terms modelling attractive and repulsive interaction potentials. Comment: 18 pages, to appear in Nonlinearity |
| Databáze: | OpenAIRE |
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