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Existence and multiplicity of solutions for the fractionalp-Laplacian Choquard logarithmic equation involving a nonlinearity with exponential critical and subcritical growth
Journal of Mathematical Physics ( IF 1.3 ) Pub Date : 2021-05-06 , DOI: 10.1063/5.0041474
Eduardo de S. Böer 1 , Olímpio H. Miyagaki 1
Affiliation  

In the present work, we obtain the existence and multiplicity of nontrivial solutions for the Choquard logarithmic equation (Δ)psu+a|u|p2u+λ(ln||*|u|p)|u|p2u=f(u)inRN, where N = sp, s ∈ (0, 1), p > 2, a > 0, λ > 0, and f:RR is a continuous nonlinearity with exponential critical and subcritical growth. We guarantee the existence of a nontrivial solution at the mountain pass level and a nontrivial ground state solution under critical and subcritical growth. Moreover, when f has subcritical growth, we prove the existence of infinitely many solutions via genus theory.

中文翻译:

涉及具有指数临界和亚临界增长的非线性的分数阶-拉普拉斯 Choquard 对数方程的解的存在性和多重性

在目前的工作中,我们获得了 Choquard 对数方程的非平凡解的存在性和多重性 (-Δ)+一种||-2+λ(输入||*||)||-2=F()一世n电阻N, 其中N = sp , s ∈ (0, 1), p > 2, a > 0, λ > 0, 并且F电阻电阻是具有指数临界和亚临界增长的连续非线性。我们保证在山口水平存在非平凡解,在临界和亚临界增长下存在非平凡基态解。此外,当f具有亚临界增长时,我们通过属论证明了无限多解的存在。
更新日期:2021-05-28
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