Results 21 to 30 of about 34,802 (260)
RADIAL SYMMETRY OF POSITIVE SOLUTIONS TO EQUATIONS INVOLVING THE FRACTIONAL LAPLACIAN [PDF]
Communications in Contemporary Mathematics, 2014 The aim of this paper is to study radial symmetry and monotonicity properties for positive solution of elliptic equations involving the fractional Laplacian. We first consider the semi-linear Dirichlet problem [Formula: see text] where (-Δ)αdenotes the fractional Laplacian, α ∈ (0, 1), and B1denotes the open unit ball centered at the origin in ℝNwith N
Felmer, Patricio, Wang, Ying
openaire +6 more sources
Positive radial solutions for a class of quasilinear Schrödinger equations in $\mathbb{R}^3$
Electronic Journal of Qualitative Theory of Differential Equations, 2022 This paper is concerned with the following quasilinear Schrödinger equations of the form: \begin{equation*} -\Delta u-u\Delta (u^2)+u=|u|^{p-2}u, \qquad x\in \mathbb{R}^3, \end{equation*} where $p\in\left(2,12\right)$.
Zhongxiang Wang, Gao Jia, Weifeng Hu
doaj +1 more source
On a radial positive solution to a nonlocal elliptic equation
Topological Methods in Nonlinear Analysis, 2003 The paper deals with Dirichlet boundary value problem for the nonlinear Poisson equation with nonlocal term \[ - \Delta u = f (u, \int_U g \circ u) \] \[ u| _{\partial U} = 0, \] where \(U\) is assumed to be an annulus or a ball. Existence of solutions is obtained via fixed point theorems for increasing compact operators.
Fijałkowski, Piotr, Przeradzki, Bogdan
openaire +3 more sources
Infinitely many radial positive solutions for nonlocal problems with lack of compactness
Electronic Journal of Qualitative Theory of Differential Equations, 2021 We are concerned with the qualitative and asymptotic analysis of solutions to the nonlocal equation $$ (-\Delta)^su+V(|z|)u=Q(|z|)u^p\quad \text{in} \ \mathbb{R}^{N},$$ where $N\geq 3 ...
Fen Zhou +2 more
doaj +1 more source
Classification of positive radial solutions to a weighted biharmonic equation
Communications on Pure and Applied Analysis, 2021 15 ...
openaire +4 more sources
Structure of Positive Radial Solutions of Semilinear Elliptic Equations
Journal of Differential Equations, 1997 This article primarily concerns uniqueness and asymptotic behavior of positive radial solutions to the semilinear problems (1) \(-\Delta u=f(u)\) in \(\mathbb{R}^n\), \(u(\infty)=0\); and (2) \(-\Delta u=f(u)\) in \(B\), \(u|_{\partial B}=0\), where \(B\) denotes a ball in \(\mathbb{R}^n\) centred at the origin, and \(f(t)= \min\{t^p,t^q\}\) for ...
Erbe, Lynn, Tang, Moxun
openaire +1 more source
Three positive radial solutions for elliptic equations in a ball
Applied Mathematics Letters, 2005 The authors consider the second-order elliptic problem of the form \[ -\Delta u=\lambda\cdot k(|x|) f(u),\quad u> 0\quad\text{in }\Omega,\quad u= a\quad\text{on }\partial\Omega,\tag{1} \] where \(\Omega\) is the ball of radius \(R_0\); \(\lambda\), \(a\) are positive parameters; \(f\in C([0,+\infty), [0,+\infty))\) is a increasing function and \(k\in C(
João Marcos do Ó +2 more
openaire +3 more sources
四川大学学报. 自然科学版, 2021 We consider the existence of positive radial solutions to a class of elliptic boundary value problem with gradient term. The existence of positive radial solutions is obtained by using the Leray-Schauder fixed point theorem.
TANG Ying, LI Yong-Xiang
doaj
Positive radial solutions to a ‘semilinear’ equation involving the Pucci's operator
Journal of Differential Equations, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Felmer Aichele, Patricio +1 more
openaire +3 more sources
Positive radial solutions involving nonlinearities with zeros
Discrete and Continuous Dynamical Systems, 2019 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Isabel Flores +2 more
openaire +2 more sources