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Partially concentrating solutions for systems with Lotka-Volterra type interactions
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DOI：10.1007/s10231-026-01662-8.png)
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Abstract
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In this paper we consider the existence of standing waves for a coupled system of k equations with Lotka-Volterra type interaction. We prove the existence of a standing wave solution with all nontrivial components satisfying a prescribed asymptotic profile. In particular, the k-1-last components of such solution exhibits a concentrating behavior, while the first one keeps a quantum nature. We analyze first in detail the result with three equations since this is the first case in which the coupling has a role contrary to what happens when only two densities appear. We also discuss the existence of solutions of this form for systems with other kind of couplings making a comparison with Lotka-Volterra type systems.
Keywords:
Nonlinear systems with Lotka-Volterra type interactions
Singularly perturbed problems
Lyapunov-Schmidt reduction
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