## The method of upper and lower solutions for second order differential inclusions with integral boundary conditions.(English)Zbl 1205.34013

The authors study a class of nonlinear boundary value problems for second order differential inclusions. In particular, they consider the problem
$x''(t)+\lambda x'(t)\in F(t,x(t)) \text{ a.e. on } T=[0,1],$
$x(0)=a, \quad x(1)=\displaystyle{\int_0^1 g(x(s))\,ds},$
where $$F:[0,1]\times \mathbb R \to 2^{\mathbb R}$$ is a Carathéodory multivalued map with non empty, compact and convex values, $$\lambda>0$$, $$a\in\mathbb R$$ and $$g:\mathbb R \to \mathbb R$$ is a continuous and nondecreasing function. By using fixed point techniques combined with the method of lower and upper solutions, the authors prove an existence result.

### MSC:

 34A60 Ordinary differential inclusions 34B15 Nonlinear boundary value problems for ordinary differential equations 47N20 Applications of operator theory to differential and integral equations
Full Text:

### References:

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