A CONJECTURE ON MULTIPLE SOLUTIONS OF A NONLINEAR ELLIPTIC BOUNDARY VALUE PROBLEM: SOME NUMERICAL EVIDENCE

作者：Hollman Lisa^*; McKenna P J

来源：Communications on Pure and Applied Analysis, 2011, 10(2): 785-802.

DOI：10.3934/cpaa.2011.10.785

• Second order elliptic boundary value problem
• nonlinear equation
• computer assisted proof
• newton's iteration
• continuation method

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.

• 出版日期2011-3