Multiplicity results for $p$-Kirchhoff modified Schrödinger equations with Stein-Weiss type critical nonlinearity in $\mathbb R^N$
نویسندگان
چکیده
In this article, we consider the following modified quasilinear critical Kirchhoff-Schrödinger problem involving Stein-Weiss type nonlinearity: $$ \mathcal K(u)= \lambda f(x) |u(x)|^{q-2} u(x)+ \Big ( \int_{\mathbb R^N}\frac{|u(y)|^{2p_{\beta,\mu}^{*}}} {|x-y|^{\mu}|y|^{\beta}}dy ) \frac {|u(x)|^{2p_{\beta,\mu}^{*}-2} u(x)}{|x|^\beta} \; \text{ in }\; \mathbb R^N, where $\lambda > 0$ is a parameter, $N\geq 3$, K(u) = a+b R^N}|\nabla u|^{p}dx \Delta_{p} u - \Delta_{p}(u^2) with $a 0$, $b\geq $\beta\geq0,$ $0 < \mu N$, 2\beta+ $2\leq q 2 p^*$. Here, $p^*=\frac{Np}{N-p}$ Sobolev exponent and $ p_{\beta,\mu}^{*}:= p2\frac{(2N-2\beta-\mu)}{N-p} respect to doubly weighted Hardy-Littlewood-Sobolev inequality (also called inequality). Then by establishing concentration-compactness argument for our problem, show existence of infinitely many nontrivial solutions equations parameter $\lambda$ using Krasnoselskii's genus theory, symmetric mountain pass theorem $\mathbb Z_2$- version different ranges $q$. We further that these belong $L^\infty(\mathbb R^N)$.
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ژورنال
عنوان ژورنال: Differential and Integral Equations
سال: 2023
ISSN: ['0893-4983']
DOI: https://doi.org/10.57262/die036-0304-247