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sub-super solution method

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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Nonlocal problems arising from the birth-jump processes
Part of
M. Delgado, A. Suárez, I. B. M. Duarte
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 149 / Issue 2 / April 2019

Published online by Cambridge University Press:

27 December 2018, pp. 447-469

Print publication:

April 2019
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In this paper, we prove the existence and uniqueness of a positive solution for a nonlocal logistic equation arising from the birth-jump processes. For this, we establish a sub-super solution method for nonlocal elliptic equations, we perform a study of the eigenvalue problems associated with these equations and we apply these results to the nonlocal logistic equation.