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- W4319316691 abstract "In this paper, we investigate the following Choquard-Kirchhoff equations in $ mathbb{R}^{N} $:$ begin{eqnarray*} left{begin{array}{l} - K_b(u) + (lambda V(x)+1)|u|^{p-2}u = left(frac{1}{|x|^{mu}} *F(u)right)f(u) mbox{in } ,mathbb{R}^{N}, u in W^{1,p}(mathbb{R}^{N}), end{array}right. end{eqnarray*} $where $ K_b(u) = biggl(1+b int_{mathbb{R}^{N}}|nabla u|^{p} dxbiggl)Delta_pu $, $ Delta_p $ is the $ p $-Laplacian operator, $ 0 < mu < p < N $, $ b, lambda $ are some positive parameters, $ f: mathbb{R} rightarrow mathbb{R} $ is a continuous function, and the potential $ V: mathbb{R}^{N} rightarrow mathbb{R} $ is a nonnegative continuous function. Under some proper conditions, by using the variational methods, we prove that the existence of multi-bump solutions for this problem if $ Omega: = mbox{int}V^{-1} left ( 0 right) $ has several isolated connected components $ Omega_{1}, cdots, Omega_{k} $ satisfying the interior of $ Omega_{j} $ is non-empty and $ partial Omega_{j} $ is smooth. Moreover, as $ lambda>0 $ large enough, the above equation has at least $ 2^{k}-1 $ multi-bump solutions." @default.
- W4319316691 created "2023-02-08" @default.
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- W4319316691 date "2023-01-01" @default.
- W4319316691 modified "2023-09-25" @default.
- W4319316691 title "On multi-bump solutions for the Choquard-Kirchhoff equations in $ mathbb{R}^{N} $" @default.
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- W4319316691 doi "https://doi.org/10.3934/dcdss.2023012" @default.
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