Abstract
In this work, we study the existence of a nontrivial bounded variation solution to a class of nonlocal elliptic problems of Kirchhoff type involving the 1-Laplacian operator in the whole space \({\mathbb {R}}^{N}\) and we will work with the space of functions of bounded variation. The Mountain Pass Theorem shows the existence of a nontrivial solution when f is an asymptotically constant nonlinearity.
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All authors contributed to the study conception and design. Material preparation and analysis were performed by Rui Liu, Lin Li and Donal OÇÖRegan. The first draft of the manuscript was written by Rui Liu and all authors commented on previous versions of the manuscript. All authors reviewed the manuscript.
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Liu, R., Li, L. & O’Regan, D. Bounded Variation Solution for a Class of Kirchhoff Type Problem Involving the 1-Laplacian Operator. Qual. Theory Dyn. Syst. 23, 24 (2024). https://doi.org/10.1007/s12346-023-00879-9
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DOI: https://doi.org/10.1007/s12346-023-00879-9