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Zbl 1048.34034
Del Toro, Naira; Roca, Francisco
Existence and multiplicity of solutions for certain Dirichlet problems with nonlinearity depending on the derivative.
(English)
[J] Nonlinear Anal., Theory Methods Appl. 55, No. 7-8, A, 827-843 (2003). ISSN 0362-546X

The authors deal with the existence and multiplicity of solutions for certain Dirichlet problems with nonlinearity depending on the derivative. More precisely, they restrict themselves to the case of bounded nonlinearities and consider $$u''(t)+ u(t)+ g(u'(t))= f(t),\quad u(0)= u(\pi)= 0,$$ where $f\in C[0,\pi]$ and $g\in C(\bbfR,\bbfR)$ with $g(\pm\infty)= \lim_{\xi\to\pm\infty} g(\xi)$ finite. Using Lyapunov-Schmidt reduction and certain asymptotical methods, the authors prove existence and multiplicity of solutions.
[Messoud A. Efendiev (Berlin)]
MSC 2000:
*34B15 Nonlinear boundary value problems of ODE

Keywords: nonlinear boundary value problems; existence of solutions; bounded nonlinearities; Dirichlet conditions

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