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This paper is concerned with the following L 2 -subcritical Kirchhoff-type equation − a + b ∫ R 2 | ∇ u | 2 d x s Δ u + V (x) u = μ u + β | u | 2 u , x ∈ R 2 , with ∫ R 2 | u | 2 d x = 1 . We give a detailed analysis of the limit property of the L 2 -normalized solution when exponent s tends toward 0 from the right (i.e., s ↘ 0 ). Our research extends previous works, in which the authors have displayed the limit behavior of L 2 -normalized solutions when s = 1 as a ↘ 0 or b ↘ 0 . [ABSTRACT FROM AUTHOR]

This paper is devoted to studying a type of elliptic equation that contains a varying nonlocal term. We provide a detailed analysis of the existence, non-existence, and blow-up behavior of L 2 -norm solutions for the related equation when the potential function V (x) fulfills an appropriate choice. [ABSTRACT FROM AUTHOR]

In this paper, we study the constrained minimization problem for an energy functional which is related to a Kirchhoff-type equation. For s = 1 , there many articles have analyzed the limit behavior of minimizers when η > 0 as b → 0 + or b > 0 as η → 0 + . When the equation involves a varying non-local term ∫ R 3 | ∇ u | 2 d x s , we give a detailed limit behavior analysis of constrained minimizers for any positive sequence { η k } with η k → 0 + . The present paper obtains an interesting result on this topic and enriches the conclusions of previous works. [ABSTRACT FROM AUTHOR]