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.
Nonlinear scalar field equation with competing nonlocal terms / D'Avenia, Pietro; Mederski, Jaroslaw; Pomponio, Alessio. - In: NONLINEARITY. - ISSN 0951-7715. - STAMPA. - 34:8(2021), pp. 5687-5707. [10.1088/1361-6544/ac0d47]
Nonlinear scalar field equation with competing nonlocal terms
Pietro d'Avenia
;Alessio Pomponio
2021
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
