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We find radial and nonradial solutions to the following nonlocal problem −Δu+ωu=Iα*F(u)f(u)−Iβ*G(u)g(u)inRN under general assumptions, in the spirit of Berestycki and Lions, imposed on f and g, where N ⩾… Click to show full abstract
We find radial and nonradial solutions to the following nonlocal problem −Δu+ωu=Iα*F(u)f(u)−Iβ*G(u)g(u)inRN under general assumptions, in the spirit of Berestycki and Lions, imposed on f and g, where N ⩾ 3, 0 ⩽ β ⩽ α < N, ω ⩾ 0, f,g:R→R are continuous functions with corresponding primitives F, G, and I α , I β are the Riesz potentials. If β > 0, then we deal with two competing nonlocal terms modelling attractive and repulsive interaction potentials.
Keywords:
competing nonlocal;
nonlocal terms;
scalar field;
field equation;
nonlinear scalar;
equation competing
Journal Title: Nonlinearity
Year Published: 2021
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Journal Title: Nonlinearity
Year Published: 2021
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!