Results 31 to 40 of about 8,578,478 (315)
New Results on the Radial Solutions to a Class of Nonlinear k-Hessian System
Journal of Mathematics, 2022 This paper investigates the positive radial solutions of a nonlinear k-Hessian system. ΛSk1/kλD2z1Sk1/kλD2z1=bxφz1,z2, x∈ℝNΛSk1/kλD2z2Sk1/kλD2z2=hxψz1,z2, x∈ℝN, where Λ is a nonlinear operator and b, h, φ, ψ are continuous functions.
Guotao Wang, Zhuobin Zhang
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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
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Positive radial solutions to classes of singular problems on the exterior domain of a ball
Journal of Mathematical Analysis and Applications, 2016 Eun Kyoung Lee, R. Shivaji, B. Son
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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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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
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Pairs of positive radial solutions for a Minkowski-curvature Neumann problem with indefinite weight [PDF]
Nonlinear Analysis, 2019 We prove the existence of a pair of positive radial solutions for the Neumann boundary value problem div ( ∇ u 1 − | ∇ u | 2 ) + λ a ( | x | ) u p = 0 , in B , ∂ ν u = 0 , on ∂ B , where B is a ball centered at the origin, a ( | x | ) is a radial sign ...
A. Boscaggin, Guglielmo Feltrin
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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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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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Rapid evaluation of radial basis functions [PDF]
, 2005 Over the past decade, the radial basis function method has been shown to produce high quality solutions to the multivariate scattered data interpolation problem.
Baxter, Brad J.C. +3 more
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, 2020 Let B be the unit ball in R N with N ≥ 2 . Let f ∈ C 1 ( [ 0 , ∞ ) , R ) , f ( 0 ) = 0 , f ( β ) = β for some β ∈ ( 0 , ∞ ) , f ( s ) s for s ∈ ( 0 , β ) , f ( s ) > s for s ∈ ( β , ∞ ) and f ′ ( β ) > λ k r , where λ k r is the k-th radial eigenvalue of
Ru-Yun Ma, Man Xu, Zhi-Qian He
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