On a Schrödinger–Kirchhoff Type Equation Involving the Fractional p-Laplacian without the Ambrosetti–Rabinowitz Condition
In this paper, we consider the existence and multiplicity of many weak solutions for the following fractional Schrödinger–Kirchhoff type equation:\begin{align*} \left(a+b\displaystyle\iint_{\mathbb{R}^{2N}}\displaystyle\frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}\mathrm{d}x\mathrm{d}y\right)^{p-1} & \...
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| Дата: | 2024 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2024
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| Теми: | |
| Онлайн доступ: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1052 |
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| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
Репозитарії
Journal of Mathematical Physics, Analysis, Geometry| Резюме: | In this paper, we consider the existence and multiplicity of many weak solutions for the following fractional Schrödinger–Kirchhoff type equation:\begin{align*} \left(a+b\displaystyle\iint_{\mathbb{R}^{2N}}\displaystyle\frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}\mathrm{d}x\mathrm{d}y\right)^{p-1} & \times (-\Delta)^s_pu+\lambda V(x)|u|^{p-2}u \\ & =f(x,u)+h(x)\ \mathrm{ in } \ \mathbb{R}^N,\end{align*}where $N > sp$, $a,b > 0$ are constants, $\lambda$ is a parameter, $(-\Delta)^s_p$ is the fractional $p$-Laplacian operator with $0 < s < 1 < p < \infty$, nonlinearity $f(x,u)$ and potential function $V (x)$ satisfy some suitable assumptions. Under those conditions, some new results are obtained for $\lambda > 0$ large enough by applying the variation methods.
Mathematical Subject Classification 2020: 35A15, 35J60, 35R11 |
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