Vladimir Polasek, Irena Rachunkova, Department of Mathematics, Palacky University, Tomkova 40, 779 00 Olomouc, Czech Republic, e-mail: polasek.vlad@seznam.cz, rachunko@inf.upol.cz
Abstract: We provide sufficient conditions for solvability of a singular Dirichlet boundary value problem with $\phi$-Laplacian
\ogather(\phi(u'))' = f(t, u, u'),
u(0) = A, u(T) = B,
where $\phi$ is an increasing homeomorphism, $\phi(\R)=\R$, $\phi(0)=0$, $f$ satisfies the Caratheodory conditions on each set $[a, b]\times\R^2$ with $[a, b]\subset(0, T)$ and $f$ is not integrable on $[0, T]$ for some fixed values of its phase variables. We prove the existence of a solution which has continuous first derivative on $[0, T]$.
Keywords: singular Dirichlet problem, $\phi$-Laplacian, existence of smooth solution, lower and upper functions
Classification (MSC 2000): 34B16, 34B15
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