共查询到20条相似文献,搜索用时 234 毫秒
1.
E. I. Abduragimov 《Russian Mathematics (Iz VUZ)》2011,55(10):1-8
We obtain sufficient conditions for the existence of a unique positive radially symmetric solution to the Dirichlet problem
for a quasilinear equation of elliptic type in a multidimensional ball. 相似文献
2.
Ar. S. Tersenov 《Journal of Applied and Industrial Mathematics》2018,12(4):770-784
We consider the Dirichlet problem for the p-Laplace equation with nonlinear gradient terms. In particular, these gradient terms cannot satisfy the Bernstein—Nagumo conditions. We obtain some sufficient conditions that guarantee the existence of a global bounded radially symmetric solution without any restrictions on the growth of the gradient term. Also we present some conditions on the function simulating the mass forces, which allow us to obtain a bounded radially symmetric solution under presence of an arbitrary nonlinear source. 相似文献
3.
Nonradial positive solutions of the ‐Laplace Emden–Fowler equation with sign‐changing weight
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Ryuji Kajikiya 《Mathematische Nachrichten》2016,289(2-3):290-299
In this paper we study the p‐Laplace Emden–Fowler equation with a radial and sign‐changing weight in the unit ball under the Dirichlet boundary condition. We show that if the weight function is negative in the unit ball except for a small neighborhood of the boundary and positive at somewhere in this neighborhood, then no least energy solution is radially symmetric. Therefore the equation has both a positive radial solution and a positive nonradial solution. Moreover, we prove in the one dimensional case that if the neighborhood is large, then a positive solution is unique. 相似文献
4.
P. Poláčik 《偏微分方程通讯》2013,38(11):1615-1638
We consider nonautonomous quasilinear parabolic equations satisfying certain symmetry conditions. We prove that each positive bounded solution u on ? N × (?∞, T) decaying to zero at spatial infinity uniformly with respect to time is radially symmetric around some origin in ? N . The origin depends on the solution but is independent of time. We also consider the linearized equation along u and prove that each bounded (positive or not) solution is a linear combination of a radially symmetric solution and (nonsymmetric) spatial derivatives of u. Theorems on reflectional symmetry are also given. 相似文献
5.
Consider the radially symmetric p-Laplacian for p?2 under zero Dirichlet boundary conditions. The main result of the present paper is that under appropriate conditions a solution of a perturbed (radially symmetric) p-Laplacian can be compared with the solution of the unperturbed one. As a consequence one obtains a sign preserving result for a system of p-Laplacians which are coupled in a nonquasimonotone way. 相似文献
6.
Margherita Nolasco 《纯数学与应用数学通讯》2003,56(12):1752-1780
We prove the existence of nontopological N‐vortex solutions for an arbitrary number N of vortex points for the self‐dual Chern‐Simons‐Higgs theory with 't Hooft “periodic” boundary conditions. We use a shadowing‐type lemma to glue together any number of single vortices obtained as a perturbation of a radially symmetric entire solution of the Liouville equation. © 2003 Wiley Periodicals, Inc. 相似文献
7.
1IntroductionInrecentyears,theexistenceandmultiplicityofsolutionsoftheproblemwerestudiedbynumerousauthors.WhereA>0,fiisasmoothdomaininR",N22.Thefundamentalquestionsaboveproblem(1.1)-(1.2):have.receivedrathersimpleanswers.Todoso,theauthorsalwaysusethenicepropertiesoftheoperatorA,forexample,thelinearity,maximumprinciple,strongmaximumprinciple,comparisonprincipleandsoon.Meanwhile,theexistenceandmultiplicityofpositiveradialsolutionsof(1.1)-(1.2)attractedmuchinterest,see[l,5-6,10,13-18]andtherefe… 相似文献
8.
Ar. S. Tersenov 《Siberian Mathematical Journal》2016,57(5):918-928
We consider the Dirichlet problem for the inhomogeneous p-Laplace equation with p nonlinear source. New sufficient conditions are established for the existence of weak bounded radially symmetric solutions as well as a priori estimates of solution and of the gradient of solution. We obtain an explicit formula that shows the dependence of the existence of these solutions on the dimension of the problem, the size of the domain, the exponent p, the nonlinear source, and the exterior mass forces. 相似文献
9.
P. Poláčik 《偏微分方程通讯》2013,38(11):1567-1593
We consider quasilinear parabolic equations on ? N satisfying certain symmetry conditions. We prove that bounded positive solutions decaying to zero at spatial infinity are asymptotically radially symmetric about a center. The asymptotic center of symmetry is not fixed a priori (and depends on the solution) but it is independent of time. We also prove a similar theorem on reflectional symmetry. 相似文献
10.
Wenrui Hao Jonathan D. Hauenstein Bei Hu Yuan Liu Yong-Tao Zhang 《Nonlinear Analysis: Real World Applications》2012,13(2):694-709
We consider a free boundary problem for a system of partial differential equations, which arises in a model of tumor growth with a necrotic core. For any positive numbers ρ<R, there exists a radially symmetric stationary solution with tumor boundary r=R and necrotic core boundary r=ρ. The system depends on a positive parameter μ, which describes the tumor aggressiveness. There also exists a sequence of values μ2<μ3<? for which branches of symmetry-breaking stationary solutions bifurcate from the radially symmetric solution branch. 相似文献
11.
Joachim Escher Anca-Voichita Matioc 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(1):1-20
The growth of tumors is an important subject in recent research. We present here a mathematical model for the growth of nonnecrotic
tumors in all the three regimes of vascularisation. This leads to a free-boundary problem which we treat by means ODE techniques.
We prove the existence of a unique radially symmetric stationary solution. It is also shown that, if the initial tumor is
radially symmetric, there exists a unique radially symmetric solution of the evolution equation, which exists for all times.
The asymptotic behaviour of this solution will be discussed in relation to the parameters characterizing cell proliferation
and cell death. 相似文献
12.
We study the isentropic compressible Navier–Stokes equations with radially symmetric data in an annular domain. We first prove the global existence and regularity results on the radially symmetric weak solutions with non‐negative bounded densities. Then we prove the global existence of radially symmetric strong solutions when the initial data ρ0, u 0 satisfy the compatibility condition for some radially symmetric g ∈ L2. The initial density ρ0 needs not be positive. We also prove some uniqueness results on the strong solutions. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
13.
建立了RN(N≥3)上一类奇异非线性双调和方程正的径向对称整体解的存在定理,并给出了解的有关性质,推广了相关文献的结果. 相似文献
14.
The existence, nonexistence and multiplicity of positive radially symmetric solutions to a class of Schrödinger–Poisson type systems with critical nonlocal term are studied with variational methods. The existence of both the ground state solution and mountain pass type solutions are proved. It is shown that the parameter ranges of existence and nonexistence of positive solutions for the critical nonlocal case are completely different from the ones for the subcritical nonlocal system. 相似文献
15.
In this paper, we study the existence of radially symmetric convex solutions for Dirichlet problems of Monge‐Ampère equations. By applying a well‐known fixed point theorem in cones, we shall establish several new criteria for the existence of nontrivial radially symmetric convex solutions for the systems of Monge‐Ampère equations with or without an eigenvalue parameter. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
16.
M. M. Babatin 《Theoretical and Mathematical Physics》2011,169(3):1767-1774
We construct an idealized spherically symmetric relativistic model of an exploding object in the framework of the theory of
surface layers in general relativity and match a Vaidya solution for a radially radiating star to another Vaidya solution
through a thin spherical shell. We reduce the equations of motion and the radiation density of the Vaidya solution given by
the matching conditions to a first-order system and analyze the general characteristics of the motion. We use a post-Newtonian
approximation to find the equation of motion of a spherically symmetric radiating shell moving in a central gravitational
potential. 相似文献
17.
YIN Huicheng 《中国科学A辑(英文版)》2000,43(3):252-266
For a class of special three-dimensional
quasilinear wave equations, we study the blowup mechanism of classical solutions. More
precisely, under the nondegenerate conditions, any radially symmetric solution with small
initial data is shown to develop singularities in the second order derivatives while the
first order derivatives and itself remain continuous, moreover the blowup of solution is
of “cusp type”. 相似文献
18.
We prove that nonnegative.so1utions to a semilinear Dirichlet problem in a ball are positive, and hence radially symmetric. In particular this answers a question in [3] where positive solutions were proven to be radially symmetric. In section 4 we provide a sufficient condition on the geometry of the .domain which ensures that nonnegative solutions are positive in the interior. 相似文献
19.
Yaniv Almog Leonid Berlyand Dmitry Golovaty Itai Shafrir 《Calculus of Variations and Partial Differential Equations》2011,42(3-4):517-546
We consider the minimization of a p-Ginzburg-Landau energy functional over the class of radially symmetric functions of degree one. We prove the existence of a unique minimizer in this class, and show that its modulus is monotone increasing and concave. We also study the asymptotic limit of the minimizers as p ?? ??. Finally, we prove that the radially symmetric solution is locally stable for 2?<?p????4. 相似文献
20.
We show the existence of standing wave solutions to the Schrödinger equation coupled with a neutral scalar field. We also verify the Chern–Simons limit for these solutions. More precisely we prove that solutions to Eqs. (1.3)–(1.4) converge to the unique positive radially symmetric solution of the nonlinear Schrödinger equation (1.6) as the coupling constant q goes to infinity. 相似文献