Abstract
We seek solutions for non-cooperative elliptic systems of two Schrödinger equations which can model phenomena in Physics and Biology. General conditions are assumed under the potentials, which produce convenient spectral properties on the elliptic operator concerned; hence, the non-cooperation characterizes it as a strongly indefinite problem. Spectral theory is employed along with an abstract linking theorem developed previously by the first two authors, which is the core of our argument. Furthermore, super- and asymptotically quadratic nonlinearities are considered.
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Research supported by FAPDF 0193.001300/2016, 0193.001765/2017, CNPq 308378/2017-2 and PROEX/CAPES, Brazil.
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Maia, L.A., Soares, M. & Ruviaro, R. Non-cooperative elliptic systems modeling interactions of Bose–Einstein condensates in \(\mathbb {R}^N\). Z. Angew. Math. Phys. 71, 105 (2020). https://doi.org/10.1007/s00033-020-01329-1
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DOI: https://doi.org/10.1007/s00033-020-01329-1