Results 71 to 80 of about 15,138,774 (296)

New multiple positive solutions for elliptic equations with singularity and critical growth

Electronic Journal of Qualitative Theory of Differential Equations, 2019
In this note, the existence of multiple positive solutions is established for a semilinear elliptic equation $ -\Delta u=\frac{\lambda}{u^\gamma}+u^{2^*-1},~x\in\Omega,~u=0, x\in\partial\Omega$, where $\Omega$ is a smooth bounded domain in $\mathbb{R}^N$
Hongmin Suo, Chunyu Lei, Jia-Feng Liao
doaj   +1 more source

Blow-Up Phenomena and Asymptotic Profiles Passing from H1-Critical to Super-Critical Quasilinear Schrödinger Equations

Advanced Nonlinear Studies, 2021
We study the asymptotic profile, as ℏ→0{\hbar\rightarrow 0}, of positive solutions ...
Cassani Daniele, Wang Youjun
doaj   +1 more source

Multiplicity and concentration of positive solutions for the fractional Schrödinger–Poisson systems with critical growth

, 2017
In this paper, we study the multiplicity and concentration of solutions for the following critical fractional Schrodinger–Poisson system: \begin{eqnarray*} \left\{ \begin{array}{ll} \epsilon^{2s}(-\triangle)^{s} {u}+ V(x)u+\phi u =f(u)+|u|^{2^*_{s}-2}u &\
Zhisu Liu, Jianjun Zhang
semanticscholar   +1 more source

Ground state solutions for nonlinear fractional Schrodinger equations involving critical growth

Electronic Journal of Differential Equations, 2017
This article concerns the ground state solutions of nonlinear fractional Schrodinger equations involving critical growth. We obtain the existence of ground state solutions when the potential is not a constant and not radial.
Hua Jin, Wenbin Liu
doaj  

Nucleation and growth by diffusion under Ostwald-Freundlich boundary condition [PDF]

, 2014
The critical radius of a nucleus grown by diffusion in a solution is studied thermodynamically as well as kinetically. The thermodynamic growth equation called Zeldovich equation of classical nucleation theory (CNT) and the kinetic diffusional growth equation combined with the Ostwald-Freundlich boundary condition lead to the same critical radius ...
arxiv   +1 more source

Multiplicity results for a class of quasilinear equations with exponential critical growth [PDF]

, 2015
In this work, we prove the existence and multiplicity of positive solutions for the following class of quasilinear elliptic equations: −εNΔNu+1+μA(x)uN−2u=f(u)inRN,u>0inRN,where ΔN is the N‐Laplacian operator, N≥2 , f is a function with exponential ...
C. O. Alves, L. R. Freitas
semanticscholar   +1 more source

Concentration Phenomena for Fractional Elliptic Equations Involving Exponential Critical Growth [PDF]

, 2015
In this paper, we deal with the singular perturbed fractional elliptic problem ε⁢(-Δ)1/2⁢u+V⁢(z)⁢u=f⁢(u)$\varepsilon(-\Delta)^{1/2}{u}+V(z)u=f(u)$ in ℝ$\mathbb{R}$, where (-Δ)1/2⁢u${(-\Delta)^{1/2}u}$ is the square root of the Laplacian and f⁢(s)${f(s)}$
C. O. Alves, J. do Ó, O. Miyagaki
semanticscholar   +1 more source

Existence of positive solutions to perturbed nonlinear Dirichlet problems involving critical growth

Electronic Journal of Differential Equations, 2017
We consider the following perturbed nonlinear elliptic problem with critical growth $$\displaylines{ -\varepsilon^2\Delta u+V(x)u=f(x)|u|^{p-2}u +\frac{\alpha}{\alpha+\beta}K(x)|u|^{\alpha-2}u|v|^\beta,\quad x\in \mathbb{R}^N,\cr -\varepsilon^2 ...
Huixing Zhang, Ran Zhang
doaj  

Sign-changing solutions for Schrödinger system with critical growth

Electronic Research Archive, 2022
We consider the following Schrödinger system $ \begin{equation*} \left\{ \begin{aligned} &-\Delta u_j = \sum\limits_{i = 1}^k \beta_{ij}|u_i|^3|u_j|u_j+\lambda_j|u_j|^{q-2}u_j, \ \ \ \text{in}\, \, \Omega, \\ &u_j = 0\quad\text{on ...
Changmu Chu, Jiaquan Liu, Zhi-Qiang Wang   +2 more
doaj   +1 more source

Effects of grain size distribution on the interstellar dust mass growth [PDF]

, 2011
Grain growth by the accretion of metals in interstellar clouds (called `grain growth') could be one of the dominant processes that determine the dust content in galaxies. The importance of grain size distribution for the grain growth is demonstrated in this paper.
arxiv   +1 more source