Developmental coordination disorder (DCD) and attention deficit/hyperactivity disorder (ADHD) are prevalent childhood disorders that frequently co-occur. Evidence from neuroimaging research suggests that children with these disorders exhibit disruptions in motor circuitry, which could account for the high rate of co-occurrence. The primary objective of this study was to investigate the functional connections of the motor network in children with DCD and/or ADHD compared to typically developing controls, with the aim of identifying common neurophysiological substrates. Resting-state fMRI was performed on seven children with DCD, 21 with ADHD, 18 with DCD + ADHD and 23 controls. Resting-state connectivity of the primary motor cortex was compared between each group and controls, using age as a co-factor. Relative to controls, children with DCD and/or ADHD exhibited similar reductions in functional connectivity between the primary motor cortex and the bilateral inferior frontal gyri, right supramarginal gyrus, angular gyri, insular cortices, amygdala, putamen, and pallidum. In addition, children with DCD and/or ADHD exhibited different age-related patterns of connectivity, compared to controls. These findings suggest that children with DCD and/or ADHD exhibit disruptions in motor circuitry, which may contribute to problems with motor functioning and attention. Our results support the existence of common neurophysiological substrates underlying both motor and attention problems.

Abstract. We prove a uniqueness result for the positive solution of A« + f(u) = 0 in R" which goes to 0 at oo . The result applies to a wide class of nonlinear functions /, including the important model case f(u) = -u + up , 1 < p < (n + 2)l(n -2). The result is proved by reducing to an initial-boundary problem for the ODE u" + (n -l)/r + f(u) = 0 and using a shooting method.

We prove a uniqueness result for the positive solution of A« + f(u) = 0 in R" which goes to 0 at oo. The result applies to a wide class of nonlinear functions /, including the important model case f(u) =-u + up , 1 < p < (n + 2)l(n-2). The result is proved by reducing to an initial-boundary problem for the ODE u" + (n-l)/r + f(u) = 0 and using a shooting method.

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