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A conjecture on multiple solutions of a nonlinear elliptic boundary value problem: some numerical evidence

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  • We investigate a conjecture regarding the number of solutions of a second order elliptic boundary value problem with an asymmetric nonlinearity. This investigation makes use of several computer assisted techniques. First, we compute approximate solutions using Newton's Iteration for small $b$ and then use a continuation method to show that the number of solutions becomes large as $b$ increases.
    Mathematics Subject Classification: Primary: 35B40, 35J25; Secondary: 35B06.


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