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- W4287994842 abstract "Given $Ngeq 3$, $1<p<N$, two measurable functions $Vleft(r right)geq 0$, $Kleft(rright)> 0$ and a continuous function $A(r) >0$ ($r>0$), we study the quasilinear elliptic equation [ -mathrm{div}left(A(|x| )|nabla u|^{p-2} nabla uright) u+Vleft( left| xright| right) |u|^{p-2}u= K(|x|) f(u) quad text{in }mathbb{R}^{N}. ] We find existence of nonegative solutions by the application of variational methods, for which we have to study the compactness of the embedding of a suitable function space $X$ into the sum of Lebesgue spaces $L_{K}^{q_{1}}+L_{K}^{q_{2}}$, and thus into $L_{K}^{q}$ ($=L_{K}^{q}+L_{K}^{q}$) as a particular case. Our results do not require any compatibility between how the potentials $A$, $V$ and $K$ behave at the origin and at infinity, and essentially rely on power type estimates of the relative growth of $V$ and $K$, not of the potentials separately. The nonlinearity $f$ has a double-power behavior, whose standard example is $f(t) = min { t^{q_1 -1}, t^{q_2 -1} }$, recovering the usual case of a single-power behavior when $q_1 = q_2$." @default.
- W4287994842 created "2022-07-26" @default.
- W4287994842 creator A5051210495 @default.
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- W4287994842 date "2019-12-13" @default.
- W4287994842 modified "2023-10-16" @default.
- W4287994842 title "Compactness and existence results for quasilinear elliptic problems with singular or vanishing potentials" @default.
- W4287994842 doi "https://doi.org/10.48550/arxiv.1912.07537" @default.
- W4287994842 hasPublicationYear "2019" @default.
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