Electron. J. Diff. Eqns., Vol. 2008(2008), No. 40, pp. 1-9.

Existence of global solutions for systems of second-order functional-differential equations with p-Laplacian

Miroslav Bartusek, Milan Medved

Abstract:
We find sufficient conditions for the existence of global solutions for the systems of functional-differential equations
$$ \big(A(t)\Phi_p(y')\big)' + B(t)g(y', y'_t) + R(t)f(y, y_t) = e(t), $$
where $\Phi_p(u) = (|u_1|^{p-1}u_1, \dots, |u_n|^{p-1}u_n)^T$ which is the multidimensional p-Laplacian.

Submitted January 29, 2008. Published March 20, 2008.
Math Subject Classifications: 34C11, 34K10.
Key Words: Second order functional-differential equation; p-Laplacian; global solution.

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Miroslav Bartusek
Department of Mathematics and Statistics
Faculty of Science, Masaryk University
Janackovo nam. 2a, CZ-602 00 Brno, Czech Republic
email: bartusek@math.muni.cz
Milan Medved
Department of Mathematical Analysis and Numerical Mathematics
Faculty of Mathematics, Physics and Informatics
Comenius University, 842 48 Bratislava, Slovakia
email: medved@fmph.uniba.sk

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