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Existence and uniqueness theorems for some fourth-order nonlinear boundary value problems. (English) Zbl 0959.34015
Summary: Let $$G$$ and $$f:[0,1] \times\mathbb{R}^4 \to\mathbb{R}$$ be two functions satisfying Carathéodory conditions. The paper is concerned with the problems of existence and uniqueness of solutions to the nonlinear fourth-order ordinary differential equation $y''''+\lambda y''+ky+ G(x,y,y', y'',y''')= f(x,y,y',y'',y''')$ with one of a particular set of boundary conditions.

##### MSC:
 34B15 Nonlinear boundary value problems for ordinary differential equations
##### Keywords:
homogeneous nonlinearity; existence; uniqueness; solutions
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