On subelliptic equations on stratified Lie groups driven by singular nonlinearity and weak L¹ data

2024/10/02 by Subhashree Sahu, Debajyoti Choudhuri, Sahu, S. +3 · 2 citations
#35J20 #35Q35 #35R35 #46E35 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2410.04418

Abstract

The article is about an elliptic problem defined on a \it stratified Lie group. Both sub- and superlinear cases are considered whose solutions are guaranteed to exist in light of the interplay between the nonlinearities and the weak L¹ datum. The existence of infinitely many solutions is proved for suitable values of λ,p,q by using the Symmetric Mountain Pass Theorem.

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• Mixed local-nonlocal p-Laplace equation with variable singular nonlinearity in the Heisenberg group
• Nonlocal singular problem and associated Sobolev type inequality with extremal in the Heisenberg group

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