Feng, Meiqiang
Published in
Advances in Nonlinear Analysis

In this paper, the equations and systems of Monge-Ampère with parameters are considered. We first show the uniqueness of of nontrivial radial convex solution of Monge-Ampère equations by using sharp estimates. Then we analyze the existence and nonexistence of nontrivial radial convex solutions to Monge-Ampère systems, which includes some new ingred...

Boţ, Radu Ioan Grad, Sorin-Mihai Meier, Dennis Staudigl, Mathias
Published in
Advances in Nonlinear Analysis

In this work we investigate dynamical systems designed to approach the solution sets of inclusion problems involving the sum of two maximally monotone operators. Our aim is to design methods which guarantee strong convergence of trajectories towards the minimum norm solution of the underlying monotone inclusion problem. To that end, we investigate ...

Wang, Ying Wei, Yuanhong
Published in
Advances in Nonlinear Analysis

Our purpose of this paper is to consider Liouville property for the fractional Lane-Emden equation (−Δ)αu=upinΩ,u=0inRN∖Ω, $$\begin{array}{} \displaystyle (-{\it\Delta})^\alpha u = u^p\quad {\rm in}\quad {\it\Omega},\qquad u = 0\quad {\rm in}\quad \mathbb{R}^N\setminus {\it\Omega}, \end{array}$$ where α ∈ (0, 1), N ≥ 1, p > 0 and Ω ⊂ ℝN–1 × [0, +∞)...

Liang, Sihua Pucci, Patrizia Zhang, Binlin
Published in
Advances in Nonlinear Analysis

In this article, we investigate multiplicity results for Choquard-Kirchhoff type equations, with Hardy-Littlewood-Sobolev critical exponents, −a+b∫RN|∇u|2dxΔu=αk(x)|u|q−2u+β∫RN|u(y)|2μ∗|x−y|μdy|u|2μ∗−2u,x∈RN, $$\begin{array}{} \displaystyle -\left(a + b\int\limits_{\mathbb{R}^N} |\nabla u|^2 dx\right){\it\Delta} u = \alpha k(x)|u|^{q-2}u + \beta\le...

Chu, Jifeng Escher, Joachim
Published in
Advances in Nonlinear Analysis

When the vorticity is monotone with depth, we present a variational formulation for steady periodic water waves of the equatorial flow in the f-plane approximation, and show that the governing equations for this motion can be obtained by studying variations of a suitable energy functional 𝓗 in terms of the stream function and the thermocline. We al...

Correa Leão, Amanda S. S. Morbach, Joelma Santos, Andrelino V. Santos Júnior, João R.
Published in
Advances in Nonlinear Analysis

Some classes of generalized Schrödinger stationary problems are studied. Under appropriated conditions is proved the existence of at least 1 + ∑i=2m $\begin{array}{} \sum_{i=2}^{m} \end{array}$ dim Vλi pairs of nontrivial solutions if a parameter involved in the equation is large enough, where Vλi denotes the eigenspace associated to the i-th eigen...

Wang, Jialin Zhu, Maochun Gao, Shujin Liao, Dongni
Published in
Advances in Nonlinear Analysis

We consider nonlinear sub-elliptic systems with VMO-coefficients for the case 1

Abdelwahed, Mohamed Chorfi, Nejmeddine
Published in
Advances in Nonlinear Analysis

The paper deals with a posteriori analysis of the spectral element discretization of a non linear heat equation. The discretization is based on Euler’s backward scheme in time and spectral discretization in space. Residual error indicators related to the discretization in time and in space are defined. We prove that those indicators are upper and l...

Zou, Weilin Li, Xinxin
Published in
Advances in Nonlinear Analysis

In this paper, we prove the existence and regularity of solutions of the homogeneous Dirichlet initial-boundary value problem for a class of degenerate elliptic equations with lower order terms. The results we obtained here, extend some existing ones of [2, 9, 11] in some sense.

Grunau, Hans-Christoph Miyake, Nobuhito Okabe, Shinya
Published in
Advances in Nonlinear Analysis

This paper is concerned with the positivity of solutions to the Cauchy problem for linear and nonlinear parabolic equations with the biharmonic operator as fourth order elliptic principal part. Generally, Cauchy problems for parabolic equations of fourth order have no positivity preserving property due to the change of sign of the fundamental solut...