Boundary value problems for fourth order differential equations in Hilbert space
The author proves existence results for two fourth-order non-degenerate two-point boundary value problems considered in real Hilbert space. The differential equation of these boundary value problems has the form \(u^{(IV)}+ f(x, u', u'', u''')= 0\), \(x\in (0, 1)\), where \(f\) satisfies some growth and compactness conditions. Moreover, if some Lipschitz type conditions hold for \(f\), then uniqueness theorems are also given. The author's approach is based on the use of the Leray-Schauder continuation theorem. Note that this paper contains improvements of several results of A. R. Aftabizadeh (1986), C. P. Gupta (1990, 1991), Y. Yang (1988).
fourth-order non-degenerate two-point boundary value problems
scientific article; zbMATH DE number 792938
scientific article