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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
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On Kirchhoff-Type Equations with Hardy Potential and Berestycki–Lions Conditions
Mathematics, 2023 The purpose of this paper is to investigate the existence and asymptotic properties of solutions to a Kirchhoff-type equation with Hardy potential and Berestycki–Lions conditions.
Hua Yang, Jiu Liu
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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
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Classification of positive radial solutions to a weighted biharmonic equation
Communications on Pure and Applied Analysis, 2021 15 ...
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Spherically symmetric solutions in Rastall gravity
上海师范大学学报. 自然科学版, 2023 In this paper， we consider the spherically symmetric solutionstothe field equation of Rastall gravity in the background of positive pressure matter.Firstly，we study the spherically symmetric solution in Rastall gravityin the background of matter with ...
XI Ping +3 more
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Plastic and Reconstructive Surgery, Global Open, 2023 Background:. The surgical plan to reconstruct the palate must be carefully prepared given the morphological peculiarity of the soft palate forming both the roof of the mouth and the floor of the nasal cavity.
Riccardo Nocini, MD +5 more
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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
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Existence of radial solutions for a p ( x ) $p(x)$ -Laplacian Dirichlet problem
Advances in Difference Equations, 2021 In this paper, using variational methods, we prove the existence of at least one positive radial solution for the generalized p ( x ) $p(x)$ -Laplacian problem − Δ p ( x ) u + R ( x ) u p ( x ) − 2 u = a ( x ) | u | q ( x ) − 2 u − b ( x ) | u | r ( x ) −
Maria Alessandra Ragusa +2 more
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Existence of Positive Ground State Solutions for Choquard Systems
Advanced Nonlinear Studies, 2020 We study the existence of positive ground state solution for Choquard systems. In the autonomous case, we prove the existence of at least one positive ground state solution by the Pohozaev manifold method and symmetric-decreasing rearrangement arguments.
Deng Yinbin, Jin Qingfei, Shuai Wei
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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
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