共查询到20条相似文献,搜索用时 31 毫秒
1.
Zhouxin Li 《Journal of Differential Equations》2019,266(11):7264-7290
We prove the existence of positive solutions of the following singular quasilinear Schrödinger equations at critical growth via variational methods, where , , , , . It is interesting that we do not need to add a weight function to control . 相似文献
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Sanming Zhou 《Journal of Pure and Applied Algebra》2019,223(3):931-947
We study two families of cyclotomic graphs and perfect codes in them. They are Cayley graphs on the additive group of , with connection sets and , respectively, where () is an mth primitive root of unity, A a nonzero ideal of , and ? Euler's totient function. We call them the mth cyclotomic graph and the second kind mth cyclotomic graph, and denote them by and , respectively. We give a necessary and sufficient condition for to be a perfect t-code in and a necessary condition for to be such a code in , where is an integer and D an ideal of containing A. In the case when , is known as an Eisenstein–Jacobi and Gaussian networks, respectively, and we obtain necessary conditions for to be a perfect t-code in , where with β dividing α. In the literature such conditions are known to be sufficient when and under an additional condition. We give a classification of all first kind Frobenius circulants of valency 2p and prove that they are all pth cyclotomic graphs, where p is an odd prime. Such graphs belong to a large family of Cayley graphs that are efficient for routing and gossiping. 相似文献
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《Discrete Mathematics》2022,345(7):112866
Let G be a graph with n vertices. A path decomposition of G is a set of edge-disjoint paths containing all the edges of G. Let denote the minimum number of paths needed in a path decomposition of G. Gallai Conjecture asserts that if G is connected, then . If G is allowed to be disconnected, then the upper bound for was obtained by Donald [7], which was improved to independently by Dean and Kouider [6] and Yan [14]. For graphs consisting of vertex-disjoint triangles, is reached and so this bound is tight. If triangles are forbidden in G, then can be derived from the result of Harding and McGuinness [11], where g denotes the girth of G. In this paper, we also focus on triangle-free graphs and prove that , which improves the above result with . 相似文献
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We study the non-linear minimization problem on with , and : where presents a global minimum α at with . In order to describe the concentration of around , one needs to calibrate the behavior of with respect to s. The model case is In a previous paper dedicated to the same problem with , we showed that minimizers exist only in the range , which corresponds to a dominant non-linear term. On the contrary, the linear influence for prevented their existence. The goal of this present paper is to show that for , and , minimizers do exist. 相似文献
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In this paper, we study the existence and concentration behavior of minimizers for , here and where and are constants. By the Gagliardo–Nirenberg inequality, we get the sharp existence of global constraint minimizers of for when , and . For the case , we prove that the global constraint minimizers of behave like for some when c is large, where is, up to translations, the unique positive solution of in and , and . 相似文献
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We consider the nonlinear problem of inhomogeneous Allen–Cahn equation where Ω is a bounded domain in with smooth boundary, ? is a small positive parameter, ν denotes the unit outward normal of ?Ω, V is a positive smooth function on . Let Γ be a curve intersecting orthogonally with ?Ω at exactly two points and dividing Ω into two parts. Moreover, Γ satisfies stationary and non-degenerate conditions with respect to the functional . We can prove that there exists a solution such that: as , approaches +1 in one part of Ω, while tends to ?1 in the other part, except a small neighborhood of Γ. 相似文献
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In this paper we study the following type of the Schrödinger–Poisson–Slater equation with critical growth where and . For the case of . We develop a novel perturbation approach, together with the well-known Mountion–Pass theorem, to prove the existence of positive ground states. For the case of , we obtain the nonexistence of nontrivial solutions by restricting the range of μ and also study the existence of positive solutions by the constrained minimization method. For the case of , we use a truncation technique developed by Brezis and Oswald [9] together with a measure representation concentration-compactness principle due to Lions [27] to prove the existence of radial symmetrical positive solutions for with some . The above results nontrivially extend some theorems on the subcritical case obtained by Ianni and Ruiz [18] to the critical case. 相似文献
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Let GP be the m-Paley graph defined on the finite field with order . We study eigenfunctions and maximal cliques in generalised Paley graphs GP , where . In particular, we explicitly construct maximal cliques of size or in GP , and show the weight-distribution bound on the cardinality of the support of an eigenfunction is tight for the smallest eigenvalue of GP . These new results extend the work of Baker et al. and Goryainov et al. on Paley graphs of square order. We also study the stability of the Erdős-Ko-Rado theorem for GP (first proved by Sziklai). 相似文献
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We study ground states of two-component Bose–Einstein condensates (BEC) with trapping potentials in , where the intraspecies interaction and the interspecies interaction ?β are both attractive, , , and β are all positive. The existence and non-existence of ground states are classified completely by investigating equivalently the associated -critical constraint variational problem. The uniqueness and symmetry-breaking of ground states are also analyzed under different types of trapping potentials as , where () is fixed and w is the unique positive solution of in . The semi-trivial limit behavior of ground states is tackled in the companion paper [12]. 相似文献
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The paper investigates longtime dynamics of the Kirchhoff wave equation with strong damping and critical nonlinearities: , with . The well-posedness and the existence of global and exponential attractors are established, and the stability of the attractors on the perturbation parameter ? is proved for the IBVP of the equation provided that both nonlinearities and are of critical growth. 相似文献
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We are concerned with the following singularly perturbed Gross–Pitaevskii equation describing Bose–Einstein condensation of trapped dipolar quantum gases: where ε is a small positive parameter, , ? denotes the convolution, and is the angle between the dipole axis determined by and the vector x. Under certain assumptions on , we construct a family of positive solutions which concentrates around the local minima of V as . Our main results extend the results in J. Byeon and L. Jeanjean (2007) [6], which dealt with singularly perturbed Schrödinger equations with a local nonlinearity, to the nonlocal Gross–Pitaevskii type equation. 相似文献
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《Discrete Mathematics》2022,345(10):113004
Let G be a graph. We say that G is perfectly divisible if for each induced subgraph H of G, can be partitioned into A and B such that is perfect and . We use and to denote a path and a cycle on t vertices, respectively. For two disjoint graphs and , we use to denote the graph with vertex set and edge set , and use to denote the graph with vertex set and edge set . In this paper, we prove that (i) -free graphs are perfectly divisible, (ii) if G is -free with , (iii) if G is -free, and (iv) if G is -free. 相似文献
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《Discrete Mathematics》2022,345(3):112717
A transversal set of a graph G is a set of vertices incident to all edges of G. The transversal number of G, denoted by , is the minimum cardinality of a transversal set of G. A simple graph G with no isolated vertex is called τ-critical if for every edge . For any τ-critical graph G with , it has been shown that by Erd?s and Gallai and that by Erd?s, Hajnal and Moon. Most recently, it was extended by Gyárfás and Lehel to . In this paper, we prove stronger results via spectrum. Let G be a τ-critical graph with and , and let denote the largest eigenvalue of the adjacency matrix of G. We show that with equality if and only if G is , , or , where ; and in particular, with equality if and only if G is . We then apply it to show that for any nonnegative integer r, we have and characterize all extremal graphs. This implies a pure combinatorial result that , which is stronger than Erd?s-Hajnal-Moon Theorem and Gyárfás-Lehel Theorem. We also have some other generalizations. 相似文献
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《Discrete Mathematics》2022,345(10):113001
The linked double star , where , is the graph consisting of the union of two stars and with a path on c vertices joining the centers. Its Ramsey number is the smallest integer r such that every 2-coloring of the edges of a admits a monochromatic . In this paper, we study the Ramsey numbers of linked double stars when c is odd. In particular, we establish bounds on the value of and determine the exact value of if , or if and . 相似文献
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Teresa DAprile 《Journal of Differential Equations》2019,266(11):7379-7415
We are concerned with the existence of blowing-up solutions to the following boundary value problem where Ω is a smooth and bounded domain in such that , is a positive smooth function, N is a positive integer and is a small parameter. Here defines the Dirac measure with pole at 0. We find conditions on the function a and on the domain Ω under which there exists a solution blowing up at 0 and satisfying as . 相似文献