Abstract
The purpose is to extend the existence result of vortex solutions to semilinear elliptic equations for a large class of nonlinearities. M. I. Weinstein used variational techniques to show the existence of nodal solutions for the specific nonlinear term ψf(¦ψ¦)=ψ(1−¦ψ¦2). An ordinary differential equation phase space setting is used to show the unique transverse intersection of unstable and stable manifolds which contain the solutions satisfying the necessary boundary conditions under certain assumptions on the nonlinearity.
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Clemons, C.B. Existence of the vortex solutions of some semilinear elliptic equations. J Dyn Diff Equat 9, 53–65 (1997). https://doi.org/10.1007/BF02219052
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DOI: https://doi.org/10.1007/BF02219052