Existence of Seven Solutions for an Asymptotically Linear Dirichlet Problem Without Symmetries
In this paper, we establish sufficient conditions for an asymptotically linear elliptic boundary value problem to have at least seven solutions. We use the mountain pass theorem, Lyapunov–Schmidt reduction arguments, existence of solutions that change sign exactly once, and bifurcation properties. No symmetry is assumed on the domain or the non-linearity.
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Castro, Alfonso (2013). "Existence of seven solutions for an asymptotically linear Dirichlet problem without symmetries". Annali di matematica pura ed applicata (0373-3114), 192 (4), p. 607. doi: 10.1007/s10231-011-0239-5