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

• Main Authors: Miroslav Bartusek, Milan Medved
• Format: Article
• Language: English
• Published: Texas State University 2008-03-01
• Series: Electronic Journal of Differential Equations
• Subjects: Second order functional-differential equation; p-Laplacian; global solution
• Online Access: http://ejde.math.txstate.edu/Volumes/2008/40/abstr.html

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