Existence and multiplicity of solutions of a kind of fourth-order boundary value problem. (English) Zbl 1076.34015
Summary: Here, existence and multiplicity results on the solutions are obtained for the fourth-order boundary value problem \(a^{(4)} (t)= f(t,u(t))\) for all \(t\in [0, 1]\) subject to \(u(0)= u(1)= u''(0)= u (1)= 0\), where \(f\) is continuous. The monotone operator theory and critical point theory are used to discuss this problem.
MSC:
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
Keywords:
Boundary value problem; Strongly monotone operator principle; Critical point theory; PS condition; Mountain pass lemmaReferences:
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