Bounded Variation Solution for a Class of Kirchhoff Type Problem Involving the 1-Laplacian Operator

• Rui Liu ^[1] ; Lin Li ^[1] ; Donal O Regan ^[2]
  1. [1] Chongqing Technology and Business University

     Chongqing Technology and Business University

     China

     
  2. [2] University of Galway
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 1, 2024
• Idioma: inglés
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• Resumen

  • 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 RN 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.