Zhang, Wen Zhang, Jian Mi, Heilong
Published in
Advances in Nonlinear Analysis

This paper is concerned with the following nonlinear Hamiltonian elliptic system with gradient term −Δu+b→(x)⋅∇u+V(x)u=Hv(x,u,v)inRN,−Δv−b→(x)⋅∇v+V(x)v=Hu(x,u,v)inRN. $$\begin{array}{} \displaystyle \left\{\,\, \begin{array}{ll} -{\it\Delta} u +\vec{b}(x)\cdot \nabla u+V(x)u = H_{v}(x,u,v)\,\,\hbox{in}\,\mathbb{R}^{N},\\[-0.3em] -{\it\Delta} v -\ve...

Wang, Xingchang Xu, Runzhang
Published in
Advances in Nonlinear Analysis

In this paper, the initial boundary value problem for a nonlocal semilinear pseudo-parabolic equation is investigated, which was introduced to model phenomena in population dynamics and biological sciences where the total mass of a chemical or an organism is conserved. The existence, uniqueness and asymptotic behavior of the global solution and the...

Binhua, Feng Chen, Ruipeng Liu, Jiayin
Published in
Advances in Nonlinear Analysis

In this paper, we study blow-up criteria and instability of normalized standing waves for the fractional Schrödinger-Choquard equation i∂tψ−(−Δ)sψ+(Iα∗|ψ|p)|ψ|p−2ψ=0. $$\begin{array}{} \displaystyle i\partial_t\psi- (-{\it\Delta})^s \psi+(I_\alpha \ast |\psi|^{p})|\psi|^{p-2}\psi=0. \end{array}$$ By using localized virial estimates, we firstly esta...

Liu, Zhenhai Papageorgiou, Nikolaos S.
Published in
Advances in Nonlinear Analysis

We consider a nonlinear parametric Dirichlet problem driven by the (p, q)-Laplacian (double phase problem) with a reaction exhibiting the competing effects of three different terms. A parametric one consisting of the sum of a singular term and of a drift term (convection) and of a nonparametric perturbation which is resonant. Using the frozen varia...

Zhang, Jian Chen, Jianhua Li, Quanqing Zhang, Wen
Published in
Advances in Nonlinear Analysis

In this paper, we study the following nonlinear Hamiltonian elliptic system with gradient term −ϵ2Δψ+ϵb→⋅∇ψ+ψ+V(x)φ=f(|η|)φ in RN,−ϵ2Δφ−ϵb→⋅∇φ+φ+V(x)ψ=f(|η|)ψ in RN, $$\begin{array}{} \displaystyle \left\{ \begin{array}{ll} -\epsilon^{2}{\it\Delta} \psi +\epsilon \vec{b}\cdot \nabla \psi +\psi+V(x)\varphi=f(|\eta|)\varphi~~\hbox{in}~\mathbb{R}^{N},...

Liang, Shuang Zheng, Shenzhou
Published in
Advances in Nonlinear Analysis

In this paper, we prove a global Calderón-Zygmund type estimate in the framework of Lorentz spaces for a variable power of the gradients to the zero-Dirichlet problem of general nonlinear elliptic equations with the nonlinearities satisfying Orlicz growth. It is mainly assumed that the variable exponents p(x) satisfy the log-Hölder continuity, whil...

Banaś, Józef Woś, Weronika
Published in
Advances in Nonlinear Analysis

The aim of the paper is to investigate the solvability of an infinite system of nonlinear integral equations on the real half-axis. The considerations will be located in the space of function sequences which are bounded at every point of the half-axis. The main tool used in the investigations is the technique associated with measures of noncompactn...

Mitrovic, D. Vujadinović, Dj.
Published in
Advances in Nonlinear Analysis

We refine a recent result on the structure of measures satisfying a linear partial differential equation 𝓐μ = σ, μ, σ are Radon measures, considering the measure μ(x) = g(x)dx + μus(x̃)(μs(x̄) + dx̄) where x = (x̃,x̄) ∈ ℝk × ℝd−k, μus is a uniformly singular measure in x̃0 and the measure μs is a singular measure. We proved that for μus-a.e. x̃0 th...

Papageorgiou, Nikolaos S. Zhang, Youpei
Published in
Advances in Nonlinear Analysis

We consider a nonlinear elliptic equation driven by the (p, q)–Laplacian plus an indefinite potential. The reaction is (p − 1)–superlinear and the boundary term is parametric and concave. Using variational tools from the critical point theory together with truncation, perturbation and comparison techniques and critical groups, we show that for all ...

Chen, Sitong Tang, Xianhua Wei, Jiuyang
Published in
Advances in Nonlinear Analysis

This paper deals with the following Choquard equation with a local nonlinear perturbation: −Δu+u=Iα∗|u|α2+1|u|α2−1u+f(u),x∈R2;u∈H1(R2), $$\begin{array}{} \displaystyle \left\{ \begin{array}{ll} - {\it\Delta} u+u=\left(I_{\alpha}*|u|^{\frac{\alpha}{2}+1}\right)|u|^{\frac{\alpha}{2}-1}u +f(u), & x\in \mathbb{R}^2; \\ u\in H^1(\mathbb{R}^2), \end{arra...