共查询到20条相似文献,搜索用时 31 毫秒
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Roberta Filippucci Patrizia Pucci Frédéric Robert 《Journal de Mathématiques Pures et Appliquées》2009,91(2):156-177
Using the Mountain-Pass Theorem of Ambrosetti and Rabinowitz we prove that admits a positive weak solution in of class , whenever , and . The technique is based on the existence of extremals of some Hardy–Sobolev type embeddings of independent interest. We also show that if is a weak solution in of , then when either , or and u is also of class . 相似文献
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Quốc Anh Ngô 《Comptes Rendus Mathematique》2017,355(5):526-532
In this note, we mainly study the relation between the sign of and in with and for . Given the differential inequality , first we provide several sufficient conditions so that holds. Then we provide conditions such that for all , which is known as the sub poly-harmonic property for u. In the last part of the note, we revisit the super poly-harmonic property for solutions to and with in . 相似文献
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Existence of standing waves of nonlinear Schrödinger equations with potentials vanishing at infinity
Ohsang Kwon 《Journal of Mathematical Analysis and Applications》2012,387(2):920-930
For a singularly perturbed nonlinear elliptic equation , , we prove the existence of bump solutions concentrating around positive critical points of V when nonnegative V is not identically zero for or nonnegative V satisfies for . 相似文献
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Consider the Hénon equation with the homogeneous Neumann boundary condition where and . We are concerned on the asymptotic behavior of ground state solutions as the parameter . As , the non-autonomous term is getting singular near . The singular behavior of for large forces the solution to blow up. Depending subtly on the dimensional measure and the nonlinear growth rate p, there are many different types of limiting profiles. To catch the asymptotic profiles, we take different types of renormalization depending on p and . In particular, the critical exponent for the Sobolev trace embedding plays a crucial role in the renormalization process. This is quite contrasted with the case of Dirichlet problems, where there is only one type of limiting profile for any and a smooth domain Ω. 相似文献
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Huei-li Lin 《Journal of Mathematical Analysis and Applications》2012,391(1):107-118
This article investigates the effect of the coefficient of the critical nonlinearity. For sufficiently small , there are at least k positive solutions of the semilinear elliptic systems where is a bounded domain, , and for . 相似文献
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We consider the Choquard equation (also known as the stationary Hartree equation or Schrödinger–Newton equation) Here stands for the Riesz potential of order , and . We prove that least energy nodal solutions have an odd symmetry with respect to a hyperplane when α is either close to 0 or close to N. 相似文献
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Soyeun Jung 《Journal of Differential Equations》2012,253(6):1807-1861
By working with the periodic resolvent kernel and the Bloch-decomposition, we establish pointwise bounds for the Green function of the linearized equation associated with spatially periodic traveling waves of a system of reaction–diffusion equations. With our linearized estimates together with a nonlinear iteration scheme developed by Johnson–Zumbrun, we obtain -behavior () of a nonlinear solution to a perturbation equation of a reaction–diffusion equation with respect to initial data in recovering and slightly sharpening results obtained by Schneider using weighted energy and renormalization techniques. We obtain also pointwise nonlinear estimates with respect to two different initial perturbations , and , , respectively, sufficiently small and sufficiently large, showing that behavior is that of a heat kernel. These pointwise bounds have not been obtained elsewhere, and do not appear to be accessible by previous techniques. 相似文献
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《Nonlinear Analysis: Theory, Methods & Applications》2005,61(5):735-758
Let be an open bounded domain, . We are concerned with the multiplicity of positive solutions of where and is a nonnegative function on . By investigating the effect of the coefficient of the critical nonlinearity, we, by means of variational method, prove the existence of multiple positive solutions. 相似文献
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This paper deals with the following nonlinear elliptic equation where , is a bounded non-negative function in . By combining a finite reduction argument and local Pohozaev type of identities, we prove that if and has a stable critical point with and , then the above problem has infinitely many solutions. This paper overcomes the difficulty appearing in using the standard reduction method to locate the concentrating points of the solutions. 相似文献
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In this paper, we consider the following elliptic equation(0.1) where , , is differentiable in and is a given nonnegative Hölder continuous function in . The asymptotic behavior at infinity and structure of separation property of positive radial solutions with different initial data for (0.1) are discussed. Moreover, the existence and separation property of infinitely many positive solutions for Hardy equation and an equation related to Caffarelli–Kohn–Nirenberg inequality are obtained respectively, as special cases. 相似文献
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In this paper, we study the following fractional Kirchhoff equations where are constants, and is the fractional Laplacian operator with , , , is real parameter. is the critical Sobolev exponent. g satisfies the Berestycki–Lions-type condition (see [2]). By using Poho?aev identity and concentration-compact theory, we show that the above problem has at least one nontrivial solution. Furthermore, the phenomenon of concentration of solutions is also explored. Our result supplements the results of Lü (see [8]) concerning the Hartree-type nonlinearity with . 相似文献
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In this article we obtain positive singular solutions of
(1)
where Ω is a small perturbation of the unit ball in . For we prove that if Ω is a sufficiently small perturbation of the unit ball there exists a singular positive weak solution u of (1). In the case of we prove a similar result but now the positive weak solution u is contained in and yet is not in for any . 相似文献
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Radu Ignat Luc Nguyen Valeriy Slastikov Arghir Zarnescu 《Comptes Rendus Mathematique》2018,356(9):922-926
For , we consider the Ginzburg–Landau functional for -valued maps defined in the unit ball with the vortex boundary data x on . In dimensions , we prove that, for every , there exists a unique global minimizer of this problem; moreover, is symmetric and of the form for . 相似文献