Existence of solutions for a 1-D boundary value problem coming from a model for burglary
(2013) Nonlinear Analysis: Real World Applications — Vol. 14, n° 5, p. 1939-1946 (2013)
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- Using Leray-Schauder degree arguments, existence results for positive solutions are proved for ordinary differential systems of the form η(x)(<sup>A-A0</sup>(x)) '-A+<sup>A0</sup>(x)+Nf(x,A)=0,<sup>N''</sup>+[g(x, A,<sup>A'</sup>)N] '-<sup>ω2</sup>(N-1)=0, with either Neumann or periodic boundary conditions. The form of the system and the assumptions upon η, <sup>A0</sup>, f and g are motivated by some mathematical models for the burglary of houses. The requested a priori estimates are obtained by some unusual combination of pointwise and <sup>L1</sup>-estimates. © 2013 Elsevier Ltd. All rights reserved.
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Garcia-Huidobro, M., Manásevich, R., & Mawhin, J. (2013). Existence of solutions for a 1-D boundary value problem coming from a model for burglary. Nonlinear Analysis: Real World Applications, 14(5), 1939-1946. https://doi.org/10.1016/j.nonrwa.2013.01.005 (Original work published 2013)