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• W2947906535 abstract "In this paper, we study the existence of multiple positive solutions to the following Kirchhoff equation with competing potential functions: $$ textstylebegin{cases} -(varepsilon ^{2}a+varepsilon b{int _{mathbb{R}^{3}}}{ vert nabla v vert } ^{2})Delta v+V(x)v=K(x) vert v vert ^{p-1}v quad mbox{in }mathbb{R}^{3}, v>0, quad vin H^{1}(mathbb{R}^{3}), end{cases} $$ where $varepsilon >0$ is a small parameter, $a,b>0$ are constants, $3< p<5$ . We relate the number of solutions with the topology of the global minima set of the function ${V^{frac{2}{p-1}-frac{1}{2}}(x)}/ {K^{frac{2}{p-1}}(x)}$ . The Nehari manifold and Ljusternik–Schnirelmann category theory are applied in our study." @default.
• W2947906535 created "2019-06-07" @default.
• W2947906535 creator A5003940092 @default.
• W2947906535 date "2019-04-30" @default.
• W2947906535 modified "2023-10-01" @default.
• W2947906535 title "Multiple positive solutions to Kirchhoff equations with competing potential functions in R 3 $mathbb{R}^{3}$" @default.
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• W2947906535 doi "https://doi.org/10.1186/s13661-019-1198-9" @default.
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