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Multiplicity of solutions for fractional equation involving the Bessel operator in RN
Mathematische Nachrichten ( IF 1 ) Pub Date : 2020-08-05 , DOI: 10.1002/mana.201800368
Nguyen Van Thin 1, 2
Affiliation  

The aim of this paper is to study the existence of solution to an equation involving the Bessel operator in R N
( I Δ ) α u + λ V ( x ) u = γ f ( x , u ) ,
where λ , γ are real positive parameters, V : R N R + is a continuous function, 0 < α < 1 with 2 α < N , f is a continuous function on R N × R which does not satisfy the Ambrosetti–Rabinowitz condition. By using the Fountain theorem and Morse theory, we obtain the existence of solutions of the above equation. In our best knowledge, it is the first time that this problem is considered.


中文翻译:

RN中涉及Bessel算子的分数阶方程的多重解

本文的目的是研究涉及Bessel算子的一个方程的解的存在性。 [R ñ
一世 - Δ α ü + λ V X ü = γ F X ü
哪里 λ γ 是真正的积极参数, V [R ñ [R + 是连续的功能 0 < α < 1个 2 α < ñ f是一个连续函数 [R ñ × [R 不满足Ambrosetti–Rabinowitz条件。通过使用Fountain定理和Morse理论,我们可以得到上述方程解的存在性。据我们所知,这是第一次考虑此问题。
更新日期:2020-10-07
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