Multiple Solutions for a Nonlinear Dirichlet Problem via - Mathematics
Multiple Solutions for a Nonlinear Dirichlet Problem via - Mathematics
Multiple Solutions for a Nonlinear Dirichlet Problem via - Mathematics
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Sketch of the Proof of Theorem A:<br />
Observe that x4 is a point of minimum of − ˆ<br />
J. Thus, dloc(∇(− ˆ<br />
J),x4) = 1<br />
and dloc(∇ ˆ<br />
J,x4) = (−1) k .<br />
In virtue of (0.7),<br />
dloc(∇J,u4) = (−1) k = 1. (0.12)<br />
MULTIPLE SOLUTIONS FOR A NONLINEAR DIRICHLET PROBLEM VIA MORSE INDEX – 33➲<br />
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