Multiplicity of Solutions for a singular Problem Involving the n-Laplacian

• Zijian Wu ^[1] ; Haibo Chen ^[1]
  1. [1] Central South University
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 2, 2024
• Idioma: inglés
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• Resumen

  • In this paper, we study the following n-Laplacian equation with singular and exponential nonlinearities ⎧ ⎪⎪⎨ ⎪⎪⎩ −nu = λu−q + u p−1 euβ |x| α in , u > 0 in , u = 0 on ∂, where is a bounded domain in Rn with smooth boundary ∂, n ≥ 2, 0 < q < 1, p > 2n, β ∈ 1, n n−1 , 0 <α< n and λ > 0 is a parameter. By analyzing the energy functional over the suitable subsets of Nehari manifold, two distinct solutions are obtained.