Abstract
We show that a superlinear boundary value problem has at least three nontrivial solutions. A pair are of one sign (positive and negative, respectively), and the third solution changes sign exactly once. The critical level of the sign-changing solution is bounded below by the sum of the two lesser levels of the one-sign solutions. If nondegenerate, the one sign solutions are of Morse index 1 and the signchanging solution has Morse index 2. Our results extend and complement those of Z.Q. Wang [12]
Original language | English (US) |
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Pages (from-to) | 1041-1053 |
Number of pages | 13 |
Journal | Rocky Mountain Journal of Mathematics |
Volume | 27 |
Issue number | 4 |
DOIs | |
State | Published - 1997 |
Keywords
- Deformation lemma
- Dirichlet problem
- Sign-changing solution
- Subcritical
- Superlinear
ASJC Scopus subject areas
- General Mathematics