Related papers: Normalized solutions for a Kirchhoff type equation…

This paper is devoted to the study of normalized solutions to the Kirchhoff type equation with a logarithmic perturbation\[-\left(a+b\int_{\mathbb{R}^3}|\nabla u|^2 \,\mathrm{d}x \right) \Delta u=\lambda u+|u|^{p-2}u+u\log u^2,\quad x…

This paper is concerned with the existence of ground states for a class of Kirchhoff type equation with combined power nonlinearities \begin{equation*} -\left(a+b\int_{\mathbb{R}^{3}}|\nabla u(x)|^{2}\right) \Delta u =\lambda…

This paper is concerned with the existence of solutions to the problem $$-\left(a+ b\int_{\mathbb{R}^{N}}|\nabla u|^{2} dx \right)\Delta u +V(x)u+\lambda u = |u|^{p-2}u,\ \ x \in \mathbb{R}^{N},\ \ \lambda \in \mathbb{R}^{+} $$ where $a,…

In this paper, we consider the existence of normalized solution to the following Kirchhoff equation with mixed Choquard type nonlinearities: \begin{equation*} \begin{cases} -\left(a + b \int_{\mathbb{R}^3} |\nabla u|^2 \, dx\right) \Delta u…

In this paper, we consider the existence and asymptotic properties of solutions to the following Kirchhoff equation \begin{equation}\label{1}\nonumber - \Bigl(a+b\int_{{\R^3}} {{{\left| {\nabla u} \right|}^2}}\Bigl) \Delta u =\lambda u+ {|…

In present paper, we study the normalized solutions $(\lambda_c, u_c)\in \R\times H^1(\R^N)$ to the following Kirchhoff problem $$ -\left(a+b\int_{\R^N}|\nabla u|^2dx\right)\Delta u+\lambda u=g(u)~\hbox{in}~\R^N,\;1\leq N\leq 3 $$…

In this paper, we study the existence of normalized solutions to the following Kirchhoff equation with a perturbation: $$ \left\{ \begin{aligned} &-\left(a+b\int _{\mathbb{R}^{N}}\left | \nabla u \right|^{2} dx\right)\Delta u+\lambda…

In this paper, we consider the following Kirchhoff type equation $$ -\left(a+ b\int_{\R^3}|\nabla u|^2\right)\triangle {u}+V(x)u=f(u),\,\,x\in\R^3, $$ where $a,b>0$ and $f\in C(\R,\R)$, and the potential $V\in C^1(\R^3,\R)$ is positive,…

In this paper, we are concerned with normalized solutions of the Kirchhoff type equation \begin{equation*} -M\left(\int_{\R^N}|\nabla u|^2\mathrm{d} x\right)\Delta u = \lambda u +f(u) \ \ \mathrm{in} \ \ \mathbb{R}^N \end{equation*} with $u…

In this paper, we investigate the existence of normalized solutions for the following nonlinear Kirchhoff type problem \begin{equation*} \begin{cases} -(a+b\int_{\Omega}\vert\nabla u\vert^2dx)\Delta u+\lambda u=\vert u\vert^{p-2}u & \text{…

In this paper, we consider the existence of solutions of the following Kirchhoff-type problem \[ \left\{ \begin{array} [c]{ll} -\left(a+b\int_{\mathbb{R}^3}|\nabla u|^2dx\right)\Delta u+ V(x)u=f(x,u),~{\rm{in}}~ \mathbb{R}^{3},\\ u\in…

In this paper, we study the following nonlinear problem of Kirchhoff type with pure power nonlinearities: (a+b\ds\int_{\R^3}|D u|^2\right)\Delta u+V(x)u=|u|^{p-1}u, u\in H^1(\R^3), u>0, $x\in \R^3, where $a,$ $b>0$ are constants, $2<p<5$…

In this paper, we study the existence and asymptotic properties of solutions to the following fractional Kirchhoff equation \begin{equation*} \left(a+b\int_{\mathbb{R}^{3}}|(-\Delta)^{\frac{s}{2}}u|^{2}dx\right)(-\Delta)^{s}u=\lambda…

In this paper, we study the existence of normalized solutions for the nonautonomous Schr\"{o}dinger-Poisson equations \begin{equation}\nonumber -\Delta u+\lambda u +\left(\vert x \vert ^{-1} * \vert u \vert ^{2} \right)…

In this paper we prove the existence of normalized solutions $(\lambda,u)\subset (0,\infty)\times H^1(\mathbb{R}^3)$ to the following Schr\"{o}dinger-Poisson equation $$ \begin{cases} -\Delta u+V(x)u+\lambda u+(|x|^{-1}\ast…

In this paper, we study a type of p-Kirchhoff equation $$ -\left( a+b\int_{\mathbb{R} ^3}{\left| \nabla u \right|^pdx} \right) \varDelta _pu=\lambda \left| u \right|^{p-2}u+\left| u \right|^{q-2}u, x \in \mathbb{R}^3 $$ with the prescribed…

In the present paper, we apply a global branch approach to study the existence, non-existence and multiplicity of positive normalized solutions $(\lambda_c, u_c)\in \mathbb{R}\times H^1(\mathbb{R}^N)$ to the following Kirchhoff problem $$…

This paper is devoted to the study of the following nonlocal equation: \begin{equation*} -\left(a+b\|\nabla u\|_{2}^{2(\theta-1)}\right) \Delta u =\lambda u+\alpha (I_{\mu}\ast|u|^{q})|u|^{q-2}u+(I_{\mu}\ast|u|^{p})|u|^{p-2}u \ \hbox{in} \…

In this paper, we study the existence of normalized solutions to the following nonlinear Schr\"{o}dinger equation \begin{equation*} \left\{ \begin{aligned} &-\Delta u=f(u)+ \lambda u\quad \mbox{in}\ \mathbb{R}^{N},\\ &u\in…

In this paper, we consider the following linearly coupled Kirchhoff--Choquard system in $\mathbb{R}^3$: \begin{align*} \begin{cases} -\left(a_1 + b_1\int_{\mathbb{R}^3} |\nabla u|^2\,dx\right)\Delta u + V_1 u = \mu (I_{\alpha} * |u|^p)…