We consider nonlocal elliptic boundary value problems of the form -A(x,u) u = λ f(u) with Dirichlet boundary conditions. We show that if f has n loops, then the problem has at least n distinct solutions, by using very simple comparison principles. Also, we study the asymptotic behavior of such solutions as the parameter λ tends to ∞.
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Chipot et al. (2014) studied this question.
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