ENTIRE SOLUTIONS OF LOTKA-VOLTERRA COMPETITION SYSTEMS WITH NONLOCAL DISPERSAL*

doi:10.1007/s10473-023-0602-9

Abstract

Abstract: This paper is mainly concerned with entire solutions of the following two-species Lotka-Volterra competition system with nonlocal (convolution) dispersals:Here $a\neq 1$, $b\neq1$, $d$, and $r$ are positive constants. By studying the eigenvalue problem of (0.1) linearized at $(\phi_c(\xi), 0)$, we construct a pair of super- and sub-solutions for (0.1), and then establish the existence of entire solutions originating from $(\phi_c(\xi), 0)$ as $t\rightarrow -\infty$, where $\phi_c$ denotes the traveling wave solution of the nonlocal Fisher-KPP equation $u_t=k*u-u+u\left(1-u\right)$. Moreover, we give a detailed description on the long-time behavior of such entire solutions as $t\rightarrow \infty$. Compared to the known works on the Lotka-Volterra competition system with classical diffusions, this paper overcomes many difficulties due to the appearance of nonlocal dispersal operators.

Key words: entire solutions, Lotka-Volterra competition systems, nonlocal dispersal, traveling waves

CLC Number:

35K57

Yuxia HAO, Wantong LI, Jiabing WANG, Wenbing XU. ENTIRE SOLUTIONS OF LOTKA-VOLTERRA COMPETITION SYSTEMS WITH NONLOCAL DISPERSAL^*[J].Acta mathematica scientia,Series B, 2023, 43(6): 2347-2376.

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ENTIRE SOLUTIONS OF LOTKA-VOLTERRA COMPETITION SYSTEMS WITH NONLOCAL DISPERSAL^*

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