共查询到20条相似文献,搜索用时 15 毫秒
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N. Hirano 《Journal of Mathematical Analysis and Applications》2005,311(2):545-566
In this paper, we consider the existence of infinitely many solutions of noncooperative elliptic systems perturbed from odd cases. 相似文献
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Clestin Wafo Soh 《Communications in Nonlinear Science & Numerical Simulation》2010,15(2):139-143
We show that the structure of the Lie symmetry algebra of a system of n linear second-order ordinary differential equations with constant coefficients depends on at most n-1 parameters. The tools used are Jordan canonical forms and appropriate scaling transformations. We put our approach to test by presenting a simple proof of the fact that the dimension of the symmetry Lie algebra of a system of two linear second-order ordinary differential with constant coefficients is either 7, 8 or 15. Also, we establish for the first time that the dimension of the symmetry Lie algebra of a system of three linear second-order ordinary differential equations with constant coefficients is 10, 12, 13 or 24. 相似文献
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A topological conjugacy is established between certain elliptic PDEs with one unbounded time direction and a simple second-order differential equation, admitting the dynamics of such PDEs to be examined on a two-dimensional submanifold. By this means, periodic solutions can be obtained to elliptic equations as perturbations of those that are independent of time. 相似文献
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We study the sublinear elliptic equation, −Δ u = |u|psgn u + f(x,u) in the bounded domain Ω under the zero Dirichlet boundary condition. We suppose that 0 < p < 1 and |f(x,u)| is small enough near u = 0 and do not suppose that f(x,u) is odd on u. Then we prove that this problem has infinitely many solutions.
Supported in part by the Grant-in-Aid for Scientific Research (C) (No. 16540179), Ministry of Education, Culture, Sports,
Science and Technology. 相似文献
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We show that any general semilinear elliptic problem with Dirichlet or Neumann boundary conditions in an annulus A⊆R2m, m?2, invariant by the action of a certain symmetry group can be reduced to a nonhomogeneous similar problem in an annulus D⊂Rm+1, invariant by another related symmetry. We apply this result to prove the existence of positive and sign changing solutions of a singularly perturbed elliptic problem in A which concentrate on one or two (m−1) dimensional spheres. We also prove that the Morse indices of these solutions tend to infinity as the parameter of concentration tends to infinity. 相似文献
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Abstract. The existence of positive radial solutions to the systems of 相似文献
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In this paper we study qualitative properties of boundary blow-up solutions to some semilinear elliptic cooperative systems in bounded non-convex domains. In particular, by a careful adaptation of the celebrated moving plane procedure of Alexandrov–Serrin, we deduce symmetry and monotonicity results for blow-up solutions for this class of systems. 相似文献
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Tomomitsu Teramoto 《Journal of Mathematical Analysis and Applications》2003,282(2):531-552
We study positive radial entire solutions of second-order quasilinear elliptic systems of the form
(∗) 相似文献
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Jesse D. Peterson Aihua W. Wood 《Journal of Mathematical Analysis and Applications》2011,384(2):284-292
We present the existence of entire large positive radial solutions for the non-monotonic system Δu=p(|x|)g(v), Δv=q(|x|)f(u) on Rn where n?3. The functions f and g satisfy a Keller-Osserman type condition while nonnegative functions p and q are required to satisfy the decay conditions and . Further, p and q are such that min(p,q) does not have compact support. 相似文献
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Zuodong YANG Qishao LU Department of Applied Mathematics Peking University of Aeronautics Astronautics Beijing China 《Communications in Nonlinear Science & Numerical Simulation》2001,6(2):88-92
1 Formulation Existence and nonexistence of solutions of the quasilinear elliptic systemhas received much attention recently (see, for example, [1-61).Problem (1) arises in the theory of quasiregular and quasiconformal mappings or in thestudy of non-Newtonian fluids. In the.latter case, the quantity (P, q) is a characteristic of themedium. Media with p > 2 and q > 2 are called dilatant fluids and those with p < 2 and q < 2are called pseudoplastics. If p = q = 2, they are Newtonian fluids.Whe… 相似文献
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Addolorata Salvatore 《Journal of Mathematical Analysis and Applications》2010,366(2):506-515
We study an elliptic system equivalent to a fourth order elliptic equation. By using variational and perturbative methods, we prove the existence of infinitely many solutions both in the symmetric and in the non-symmetric case. 相似文献
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Marcelo F. Furtado Francisco O.V. de Paiva 《Journal of Mathematical Analysis and Applications》2006,319(2):435-449
We establish the existence and multiplicity of solutions for some resonant elliptic systems. The results are proved by applying minimax arguments and Morse theory. 相似文献
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This paper is devoted to investigate multiple positive solutions to a singular elliptic system where the nonlinearity involves a combination of concave and convex terms. By exploiting the effect of the coefficient of the critical nonlinearity and a variational method, we establish the main result which is based on the argument of the compactness. 相似文献
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HanZhaoxiu 《分析论及其应用》2003,19(2):145-152
By considering the properties of f(t,u,v)/u v, g(t,u,v)/u v, we show the multiplicity of at least two positive solutions of the elliptic system. 相似文献
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《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2014,31(6):1155-1173
This paper is concerned with stability analysis of asymptotic profiles for (possibly sign-changing) solutions vanishing in finite time of the Cauchy–Dirichlet problems for fast diffusion equations in annuli. It is proved that the unique positive radial profile is not asymptotically stable, and moreover, it is unstable for the two-dimensional annulus. Furthermore, the method of stability analysis presented here will be also applied to exhibit symmetry breaking of least energy solutions. 相似文献
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Yuanji Cheng 《Czechoslovak Mathematical Journal》1997,47(4):681-687
In this paper, we consider the existence and nonexistence of positive solutions of degenerate elliptic systems
where –p is the p-Laplace operator, p > 1 and is a C
1,-domain in
. We prove an analogue of [7, 16] for the eigenvalue problem with
and obtain a non-existence result of positive solutions for the general systems. 相似文献
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In this paper we consider the question of nonexistence of nontrivial solutions for nonlinear elliptic systems involving fractional diffusion operators. Using a weak formulation approach and relying on a suitable choice of test functions, we derive sufficient conditions in terms of space dimension and systems parameters. Also, we present three main results associated to three different classes of systems. 相似文献
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D. D. Hai 《Proceedings of the American Mathematical Society》2005,133(1):223-228
We obtain necessary and sufficient conditions for the existence of positive solutions for a class of sublinear Dirichlet quasilinear elliptic systems.