共查询到20条相似文献,搜索用时 768 毫秒
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We study the stationary Stokes system in divergence form. The coefficients are assumed to be merely measurable in one direction and have Dini mean oscillations in the other directions. We prove that if is a weak solution of the system, then is bounded and its certain linear combinations are continuous. We also prove a weak type- estimate for under a stronger assumption on the -mean oscillation of the coefficients. The corresponding results up to the boundary on a half ball are also established. These results are new even for elliptic equations and systems. 相似文献
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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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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 an initial-value problem based on a class of scalar nonlinear hyperbolic reaction–diffusion equations of the general form in which x and τ represent dimensionless distance and time respectively and is a parameter related to the relaxation time. Furthermore the reaction function, , is given by the bistable cubic polynomial, in which is a parameter. The initial data is given by a simple step function with for and for . It is established, via the method of matched asymptotic expansions, that the large-time structure of the solution to the initial-value problem involves the evolution of a propagating wave front which is either of reaction–diffusion or of reaction–relaxation type. The one exception to this occurs when in which case the large time attractor for the solution of the initial-value problem is a stationary state solution of kink type centred at the origin. 相似文献
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Rafael López 《Journal of Differential Equations》2019,266(7):3927-3941
We consider a smooth solution of the singular minimal surface equation defined in a bounded strictly convex domain of with constant boundary condition. If , we prove the existence a unique critical point of u. We also derive some and estimates of u by using the theory of maximum principles of Payne and Philippin for a certain family of Φ-functions. Finally we deduce an existence theorem of the Dirichlet problem when . 相似文献
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We provide an entropy formulation for porous medium-type equations with a stochastic, non-linear, spatially inhomogeneous forcing. Well-posedness and -contraction is obtained in the class of entropy solutions. Our scope allows for porous medium operators for all , and Hölder continuous diffusion nonlinearity with exponent 1/2. 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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Chen Huang 《Journal of Mathematical Analysis and Applications》2022,505(2):125496
This paper considers the following general form of quasilinear elliptic equation with a small perturbation: where is a bounded domain with smooth boundary and small enough. We assume the main term in the equation to have a mountain pass structure but do not suppose any conditions for the perturbation term . Then we prove the equation possesses a positive solution, a negative solution and a sign-changing solution. Moreover, we are able to obtain the asymptotic behavior of these solutions as . 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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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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《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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This paper studies the asymptotic behavior of smooth solutions to the generalized Hall-magneto-hydrodynamics system (1.1) with one single diffusion on the whole space . We establish that, in the inviscid resistive case, the energy vanishes and converges to a constant as time tends to infinity provided the velocity is bounded in ; in the viscous non-resistive case, the energy vanishes and converges to a constant provided the magnetic field is bounded in . In summary, one single diffusion, being as weak as or with small enough , is sufficient to prevent asymptotic energy oscillations for certain smooth solutions to the system. 相似文献
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Qingbo Huang 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2019,36(7):1869-1902
We develop interior and regularity theories for -viscosity solutions to fully nonlinear elliptic equations , where T is approximately convex at infinity. Particularly, regularity theory holds if operator T is locally semiconvex near infinity and all eigenvalues of are at least as . regularity for some Isaacs equations is given. We also show that the set of fully nonlinear operators of regularity theory is dense in the space of fully nonlinear uniformly elliptic operators. 相似文献
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