## Remarks on the range properties of certain semilinear problems of Landesman-Lazer type.(English)Zbl 0993.34012

The authors consider the Dirichlet problem $u''(t)+ u(t)+ g(u'(t))= f(t),\quad u(0)= u(\pi)= 0.$ It is assumed that $$g$$ is continuous, has finite limits $$g(+\infty)$$, $$g(-\infty)$$, and $$g(-\infty)< g(s)< g(+\infty)$$ for all $$s$$. The case of odd and increasing $$g$$ with some asymptotic conditions is dealt with in more detail. The structure of the set of continuous functions $$f$$ is studied for which the problem is solvable.

### MSC:

 34B15 Nonlinear boundary value problems for ordinary differential equations

### Keywords:

Dirichlet problem; bounded nonlinearities
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### References:

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