## Existence and uniqueness of solutions for a fourth-order boundary value problem.(English)Zbl 1169.34308

Summary: We study the fourth-order two-point boundary value problem
\begin{aligned} & x''''(t)-f(t,x(t),x'(t),x'',x'''(t))=0,\quad t\in(0,1),\\ & x(0)=x'(1)=0,\quad ax''(0)-bx'''(0)=0,\quad cx''(1)+dx'''(1)=0.\end{aligned}
By means of lower and upper solution method, growth conditions on the nonlinear term $$f$$ which guarantee the existence of solutions for the above boundary value problem are given. In particular, we obtain the uniqueness of the solution by imposing a monotonicity condition of the term $$f$$.

### MSC:

 34B15 Nonlinear boundary value problems for ordinary differential equations 47N20 Applications of operator theory to differential and integral equations
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### References:

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