We study a second order nonlinear system driven by the vector $p$-Laplacian, with a multivalued nonlinearity and defined on the positive time semi-axis $\mathbb{R}_+.$ Using degree theoretic techniques we solve an auxiliary mixed boundary value problem defined on the finite interval $[0,n]$ and then via a diagonalization method we produce a solution for the original infinite time-horizon system.

Keywords:

semi-infinity interval, vector $p$-Laplacian, multivalued nonlinear, fixed point index, Hartman condition, completely continuous map semi-infinity interval, vector $p$-Laplacian, multivalued nonlinear, fixed point index, Hartman condition, completely continuous map

MSC Classifications:

34A60 show english descriptions Differential inclusions [See also 49J21, 49K21] 34A60 - Differential inclusions [See also 49J21, 49K21]

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