Infinitely many solutions for The Brézis-Nirenberg problem with nonlinear Choquard equations

He, Rui

doi:10.1016/j.jmaa.2022.126426

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2024

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“…for n large enough.Similar to[16, Lemma 4.3], we can prove that the index set Λ ∞ in the profile decomposition (4.26) is empty.The proof part 3 of Theorem 4.1. Note that Λ ∞ is empty, the profile decomposition in (4.26) reduces tou n = k∈Λ1 U k (• − y n,k ) + r n ,(4.50)where r n → 0 in L 2 * (R N ) as n → ∞.…”

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confidence: 60%

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Localized nodal solutions for semiclassical Choquard equations with critical growth

Zhang,

Zhang

2024

ejde

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In this article, we study the existence of localized nodal solutions for semiclassical Choquard equation with critical growth $$ -\epsilon^2 \Delta v +V(x)v = \epsilon^{\alpha-N}\Big(\int_{R^N} \frac{|v(y)|^{2_\alpha^*}}{|x-y|^{\alpha}}\,dy\Big) |v|^{2_\alpha^*-2}v +\theta|v|^{q-2}v,\; x \in R^N, $$ where $\theta>0$, $N\geq 3$, $0< \alpha<\min \{4,N-1\},\max\{2,2^*-1\}< q< 2 ^*$, $2_\alpha^*= \frac{2N-\alpha}{N-2}$, $V$ is a bounded function. By the perturbation method and the method of invariant sets of descending flow, we establish for small $\epsilon$ the existence of a sequence of localized nodal solutions concentrating near a given local minimum point of the potential function $V$. For more information see https://ejde.math.txstate.edu/Volumes/2024/19/abstr.html

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“…Combining perturbation method, truncation method and the method of invariant sets of descending flow, we prove (1.10) possesses a sequence of localized nodal solutions. As for the method mentioned, we refer [49,45,16] and the references therein.…”

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confidence: 99%

Localized nodal solutions for semiclassical Choquard equations with critical growth

Zhang,

Zhang

2024

ejde

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Infinitely many solutions for The Brézis-Nirenberg problem with nonlinear Choquard equations

Cited by 1 publication

References 37 publications

Localized nodal solutions for semiclassical Choquard equations with critical growth

Localized nodal solutions for semiclassical Choquard equations with critical growth

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