MATHEMATICA BOHEMICA, Vol. 130, No. 4, pp. 409-425 (2005)

Singular Dirichlet problem for ordinary differential equations with $\unusedphi$-Laplacian

Vladimir Polasek, Irena Rachunkova

Vladimir Polasek, Irena Rachunkova, Department of Mathematics, Palacky University, Tomkova 40, 779 00 Olomouc, Czech Republic, e-mail:,

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 Carath{é}odory 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 (MSC2000): 34B16, 34B15

Full text of the article:

[Previous Article] [Contents of this Number] [Journals Homepage]
© 2005–2010 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition