Multiple solutions of some nonlinear fourth-order beam equations. (English) Zbl 1145.34008
Summary: Several new existence theorems on three solutions and infinitely many solutions for the following fourth-order beam equation are obtained:
\[ u^{(4)}=f(t,u(t)),\quad t\in[0,1]; \quad u(0)=u(1)=u''(0)=u''(1)=0, \]
where \(f\in C^1([0,1]\times \mathbb R^1,\mathbb R^1)\). The Morse theory is employed to discuss this problem.
\[ u^{(4)}=f(t,u(t)),\quad t\in[0,1]; \quad u(0)=u(1)=u''(0)=u''(1)=0, \]
where \(f\in C^1([0,1]\times \mathbb R^1,\mathbb R^1)\). The Morse theory is employed to discuss this problem.
MSC:
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
| 58E05 | Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces |
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