Abstract:This paper is concerned with the nonlocal dispersal equations with inhomogeneous bistable nonlinearity in one dimension. The varying nonlinearity consists of two spatially independent bistable nonlinearities, which are connected by a compact transition region. We establish the existence of a unique entire solution connecting two traveling wave solutions pertaining to the different nonlinearities. In particular, we use a "squeezing" technique to show that the traveling wave of the equation with one nonlinearity… Show more
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