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Existence and multiplicity of solutions for certain Dirichlet problems with nonlinearity depending on the derivative. (English) Zbl 1048.34034
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.

34B15Nonlinear boundary value problems for ODE
Full Text: DOI
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