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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 ODE
Full Text:
References:
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