Multiple Solutions for a Nonlinear Dirichlet Problem via - Mathematics

Sketch of the Proof of Theorem A:
Let K be the set of critical points of J. Let S1, S2, S3 be disjoint open
bounded regions in H such that S1 ∩ K = {u1}, S2 ∩ K is the set of
positive solutions of (1), and S3 ∩ K is the set of negative solutions of
(0.1). We consider two cases, which will lead us to prove (b) and (d) of
Theorem A.
MULTIPLE SOLUTIONS FOR A NONLINEAR DIRICHLET PROBLEM VIA MORSE INDEX – 35➲
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