Related papers: Normalized solutions to a class of Kirchhoff equat…

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 the present paper, we study the existence of normalized solutions to the following Kirchhoff type equations \begin{equation*} -\left(a+b\int_{\R^3}|\nabla u|^2\right)\Delta u+V(x)u+\lambda u=g(u)~\hbox{in}~\R^3 \end{equation*} satisfying…

The following well-known Kirchhoff equation with the Sobolev critical exponent has been extensively studied, \begin{equation*} -\Big(a+b\int_{\mathbb R^N} | \nabla u|^2dx\Big) \Delta u+\lambda u=\mu |u|^{q-2}u+|u|^{2^*-2}u \ \ {\rm in}\ \…

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 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…

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 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…

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 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 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 study the existence and regularity results of normalized solutions to the following quasilinear elliptic Choquard equation with critical Sobolev exponent and mixed diffusion type operators: \begin{equation*}…

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 following nonlinear problem of Kirchhoff type with critical Sobolev exponent: -\left(a+b\ds\int_{\R^3}|D u|^2\right)\Delta u+u=f(x,u)+u^{5}, u\in H^1(\R^3), u>0, $x\in \R^3$ where a,b>0 are constants. Under…

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{…

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} \…

We study asymptotic behavior of positive ground state solutions of the nonlinear Kirchhoff equation $$ -\Big(a+b\int_{\mathbb R^N}|\nabla u|^2\Big)\Delta u+ \lambda u= u^{q-1}+ u^{p-1} \quad {\rm in} \ \mathbb R^N, $$ as $\lambda\to 0$ and…

In this paper, we consider the existence and multiplicity of normalized solutions for the following $p$-Laplacian critical equation \begin{align*} \left\{\begin{array}{ll} -\Delta_{p}u=\lambda\lvert u\rvert^{p-2}u+\mu\lvert…

In this paper, we consider the existence of positive solutions with prescribed $L^2$-norm for the following nonlinear Schr\"{o}dinger equation involving potential and Sobolev critical exponent \begin{equation*} \begin{cases} -\Delta…

In this paper, we study the existence of normalized solutions for the following quasilinear Schr\"odinger equation with Sobolev critical exponent: \begin{eqnarray*} -\Delta u-u\Delta (u^2)+\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,…