相关论文: Multiplicity and uniform estimate for a class of v…

In this article, we study the existence/multiplicity results for the following variable order nonlocal Choquard problem with variable exponents (-\Delta)_{p(\cdot)}^{s(\cdot)}u(x)&=\lambda|u(x)|^{\alpha(x)-2}u(x)+…

In this article, first we address the regularity of weak solution for a class of $p$-fractional Choquard equations: \begin{equation*} \;\;\; \left.\begin{array}{rl}…

In this article, we study the following nonlinear doubly nonlocal problem involving the fractional Laplacian in the sense of Hardy-Littlewood-Sobolev inequality \begin{equation*} \left\{\begin{aligned} (-\Delta)^s u & =…

We investigate the following fractional $p$-Laplacian equation \[ \begin{cases} \begin{aligned} (-\Delta)_p^s u&=\lambda |u|^{q-2}u+|u|^{p_s^*-2}u &&\text{in}~\Omega,\\ u &=0 &&\text{in}~ \mathbb{R}^n\setminus\Omega, \end{aligned}…

We prove the existence of solutions for the following critical Choquard type problem with a variable-order fractional Laplacian and a variable singular exponent \begin{align*} \begin{split} a(-\Delta)^{s(\cdot)}u+b(-\Delta)u&=\lambda…

In this work, we study the existence and multiplicity of solutions for the following problem \begin{equation}\label{probaa1} \left\{ \begin{aligned} -(\Delta)_{p}^{s} u + V(x)|u|^{p-2}u &= \lambda f(u),&x\in\Omega; u&=0,&x\in…

We consider the following doubly nonlocal nonlinear logistic problem driven by the fractional $p$-Laplacian \begin{equation*} \pl u = f(x,u) -\cq ~\text{in}~ \O, ~u=0 ~\text{in}~ \Rn\setminus\O. \end{equation*} Here $ \O \subset \Rn…

In this paper, we investigate the following fractional Choquard type equation: \[ (- \Delta)_p^s\, u = \lambda\frac{|u|^{r-2}u}{|x|^\alpha}\,+\gamma \big(\int_\Omega \frac{|u|^q}{|x-y|^\mu}dy\big) |u|^{q-2}u \ \ \text{in } \Omega,\ \ u = 0…

This article deals with the study of the following nonlinear doubly nonlocal equation: \begin{equation*} (-\Delta)^{s_1}_{p}u+\ba(-\Delta)^{s_2}_{q}u = \la a(x)|u|^{\delta-2}u+ b(x)|u|^{r-2} u,\; \text{ in }\; \Om, \; u=0 \text{ on }…

In this paper we deal with the following fractional Choquard equation \begin{equation*} \left\{ \begin{array}{ll} \varepsilon^{sp}(-\Delta)^{s}_{p} u + V(x)|u|^{p-2}u = \varepsilon^{\mu-N}\left(\frac{1}{|x|^{\mu}}*F(u)\right)f(u) \mbox{ in…

In the present work we obtain the existence and multiplicity of nontrivial solutions for the Choquard logarithmic equation $(-\Delta)_{p}^{s}u + |u|^{p-2}u + (\ln|\cdot|\ast |u|^{p})|u|^{p-2}u = f(u) \textrm{ \ in \ } \mathbb{R}^N $ , where…

In this paper, we study existence and multiplicity of solutions for the following Kirchhoff-Choquard type equation involving the fractional $p$-Laplacian on the Heisenberg group: \begin{equation*} \begin{array}{lll}…

We investigate the existence of normalized solutions for the following nonlinear fractional Choquard equation: $$ (-\Delta)^s u+V(\epsilon x)u=\lambda u+\left(I_\alpha *|u|^q\right)|u|^{q-2} u+\left(I_\alpha *|u|^p\right)|u|^{p-2} u, \quad…

We consider the following nonlinear Choquard equation with Dirichlet boundary condition $$-\Delta u =\left(\int_{\Omega}\frac{|u|^{2_{\mu}^{\ast}}}{|x-y|^{\mu}}dy\right)|u|^{2_{\mu}^{\ast}-2}u+\lambda…

We prove the existence of infinitely many nonnegative solutions to the following nonlocal elliptic partial differential equation involving singularities \begin{align} (-\Delta)_{p(\cdot)}^{s}…

In the present paper, we establish a multiplicity result for a following class of nonlocal Neumann eigenvalue problems involving the fractional p-Laplacian. \begin{align} \begin{cases} (-\Delta)^{s}_{p}u + a(x) \abs{u}^{p-2}u =\lambda…

In this article using Nehari manifold method we study the multiplicity of solutions of the following nonlocal elliptic system involving variable exponents and concave-convex nonlinearities: \begin{equation*} \;\;\; \begin{array}{rl}…

In this work, we have proved a version of the Hardy-Littlewood-Sobolev inequality for variable exponents. After we use the variational method to establish the existence of solution for a class of Choquard equations involving the…

In this paper, we show the existence and multiplicity of nontrivial, non-negative solutions of the fractional $p$-Kirchhoff problem \begin{equation*} \begin{array}{rllll}…

We will prove multiplicity results for the mixed local-nonlocal elliptic equation of the form \begin{eqnarray} \begin{split} -\Delta_pu+(-\Delta)_p^s u&=\frac{\lambda}{u^{\gamma}}+u^r \text { in } \Omega, \\u&>0 \text{ in } \Omega,\\u&=0…