Meng, Yuxi Zhang, Xinrui He, Xiaoming
Published in
Advances in Nonlinear Analysis

In this paper, we study the fractional Schrödinger-Poisson system (−Δ)su+V(x)u+K(x)ϕ|u|q−2u=h(x)f(u)+|u|2s∗−2u,in R3,(−Δ)tϕ=K(x)|u|q,in R3, $$\begin{array}{} \displaystyle \left\{ \begin{array}{ll} (-{\it\Delta})^{s}u+V(x)u+ K(x) \phi|u|^{q-2}u=h(x)f(u)+|u|^{2^{\ast}_{s}-2}u,&\mbox{in}~ {\mathbb R^{3}},\\ (-{\it\Delta})^{t}\phi=K(x)|u|^{q},&\mbox{i...

Wang, Yong Wu, Wenpei
Published in
Advances in Nonlinear Analysis

We study the initial-boundary value problems of the three-dimensional compressible elastic Navier-Stokes-Poisson equations under the Dirichlet or Neumann boundary condition for the electrostatic potential. The unique global solution near a constant equilibrium state in H2 space is obtained. Moreover, we prove that the solution decays to the equilib...

Cuesta, Eduardo Kirane, Mokhtar Alsaedi, Ahmed Ahmad, Bashir
Published in
Advances in Nonlinear Analysis

We consider a fractional derivative with order varying in time. Then, we derive for it a Leibniz' inequality and an integration by parts formula. We also study an initial value problem with our time variable order fractional derivative and present a regularity result for it, and a study on the asymptotic behavior.

Hyder, Ali Yang, Wen
Published in
Advances in Nonlinear Analysis

We analyze stable weak solutions to the fractional Geľfand problem (−Δ)su=euinΩ⊂Rn. $$\begin{array}{} \displaystyle (-{\it\Delta})^su = e^u\quad\mathrm{in}\quad {\it\Omega}\subset\mathbb{R}^n. \end{array}$$ We prove that the dimension of the singular set is at most n − 10s.

Alaa, Nour Eddine Aqel, Fatima Taourirte, Laila
Published in
Advances in Nonlinear Analysis

The aim of this work is to study a quasilinear elliptic equation with singular nonlinearity and data measure. Existence and non-existence results are obtained under necessary or sufficient conditions on the data, where the main ingredient is the isoperimetric inequality. Finally, uniqueness results for weak solutions are given.

Acharya, A. Fonseka, N. Quiroa, J. Shivaji, R.
Published in
Advances in Nonlinear Analysis

We study positive solutions to the steady state reaction diffusion equation of the form: −Δu=λf(u); Ω∂u∂η+λu=0; ∂Ω $$\begin{array}{} \displaystyle \left\lbrace \begin{matrix} -{\it\Delta} u =\lambda f(u);~ {\it\Omega} \\ \frac{\partial u}{\partial \eta}+ \sqrt{\lambda} u=0;~\partial {\it\Omega}\end{matrix} \right. \end{array}$$ where λ > 0 is a pos...

Jleli, Mohamed Samet, Bessem Vetro, Calogero
Published in
Advances in Nonlinear Analysis

We study the wave inequality with a Hardy potential ∂ttu−Δu+λ|x|2u≥|u|pin (0,∞)×Ω, $$\begin{array}{} \displaystyle \partial_{tt}u-{\it\Delta} u+\frac{\lambda}{|x|^2}u\geq |u|^p\quad \mbox{in } (0,\infty)\times {\it\Omega}, \end{array}$$ where Ω is the exterior of the unit ball in ℝN, N ≥ 2, p > 1, and λ ≥ − N−222 $\begin{array}{} \displaystyle \lef...

Tao, Qiang Zhu, Canze
Published in
Advances in Nonlinear Analysis

This paper deals with a Cauchy problem of the full compressible Hall-magnetohydrodynamic flows. We establish the existence and uniqueness of global solution, provided that the initial energy is suitably small but the initial temperature allows large oscillations. In addition, the large time behavior of the global solution is obtained.

Díaz, J. I. Feo, F. Posteraro, M. R.
Published in
Advances in Nonlinear Analysis

We consider a class of semilinear equations with an absorption nonlinear zero order term of power type, where elliptic condition is given in terms of Gauss measure. In the case of the superlinear equation we introduce a suitable definition of solutions in order to prove the existence and uniqueness of a solution in ℝN without growth restrictions at...

Lei, Chun-Yu Liao, Jia-Feng
Published in
Advances in Nonlinear Analysis

In this paper, we consider a class of semilinear elliptic equation with critical exponent and -1 growth. By using the critical point theory for nonsmooth functionals, two positive solutions are obtained. Moreover, the symmetry and monotonicity properties of the solutions are proved by the moving plane method. Our results improve the corresponding r...