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- W4385373756 abstract "In this paper we study the existence of bound states of the following class of quasilinear problems, begin{equation*} left{ begin{aligned} &-varepsilon ^pDelta_pu+V(x)u^{p-1}=f(u)+u^{p^ast -1}, u>0, text{in} mathbb{R}^{N}, &lim _{|x|rightarrow infty }u(x) = 0 , end{aligned} right. end{equation*} where $varepsilon>0$ is small, $1<p<N,$ $f$ is a nonlinearity with general subcritical growth in the Sobolev sense, $p^{ast } = pN/(N-p)$ and $V$ is a continuous nonnegative potential. By introducing a new set of hypotheses, our analysis includes the critical frequency case which allows the potential $V$ to not be necessarily bounded below away from zero. We also study the regularity and behavior of positive solutions as $|x|rightarrow infty$ or $varepsilon rightarrow 0,$ proving that they are uniformly bounded and concentrate around suitable points of $mathbb{R}^N,$ that may include local minima of $V$." @default.
- W4385373756 created "2023-07-29" @default.
- W4385373756 creator A5087392897 @default.
- W4385373756 date "2023-07-26" @default.
- W4385373756 modified "2023-10-16" @default.
- W4385373756 title "Existence of bound states for quasilinear elliptic problems involving critical growth and frequency" @default.
- W4385373756 doi "https://doi.org/10.48550/arxiv.2307.14462" @default.
- W4385373756 hasPublicationYear "2023" @default.
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