共查询到20条相似文献,搜索用时 31 毫秒
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Ryuji Kajikiya 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(7):2117-2131
In this paper, a superlinear elliptic equation whose coefficient diverges on the boundary is studied in any bounded domain Ω under the zero Dirichlet boundary condition. Although the equation has a singularity on the boundary, a solution is smooth on the closure of the domain. Indeed, it is proved that the problem has a positive solution and infinitely many solutions without positivity, which belong to or . Moreover, it is proved that a positive solution has a higher order regularity up to . 相似文献
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Wolfgang Reichel 《Journal of Differential Equations》2010,248(7):1866-680
We consider the 2m-th order elliptic boundary value problem Lu=f(x,u) on a bounded smooth domain Ω⊂RN with Dirichlet boundary conditions on ∂Ω. The operator L is a uniformly elliptic linear operator of order 2m whose principle part is of the form . We assume that f is superlinear at the origin and satisfies , , where are positive functions and q>1 is subcritical. By combining degree theory with new and recently established a priori estimates, we prove the existence of a nontrivial solution. 相似文献
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In this paper we prove the local and global well-posedness of a dissipative nonlinear electrohydrodynamic system in modulation spaces under certain conditions of s, q, and σ. 相似文献
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Liang Zhao 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(1):433-443
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This paper deals with localized parabolic equations , with homogeneous Dirichlet boundary conditions, where x0 is any fixed point in a bounded domain of RN. The optimal classification of non-simultaneous and simultaneous blow-up phenomena is proposed for all of the nonnegative exponents. Moreover, uniform blow-up profiles are obtained for all kinds of simultaneous blow-up solutions. 相似文献
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Let (X,T) be a topological dynamical system and be a sub-additive potential on C(X,R). Let U be an open cover of X. Then for any T-invariant measure μ, let . The topological pressure for open covers U is defined for sub-additive potentials. Then we have a variational principle:
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Let s∈R. In this paper, the authors first establish the maximal function characterizations of the Besov-type space with and τ∈[0,∞), the Triebel-Lizorkin-type space with p∈(0,∞), q∈(0,∞] and τ∈[0,∞), the Besov-Hausdorff space with p∈(1,∞), q∈[1,∞) and and the Triebel-Lizorkin-Hausdorff space with and , where t′ denotes the conjugate index of t∈[1,∞]. Using this characterization, the authors further obtain the local mean characterizations of these function spaces via functions satisfying the Tauberian condition and establish a Fourier multiplier theorem on these spaces. All these results generalize the existing classical results on Besov and Triebel-Lizorkin spaces by taking τ=0 and are also new even for Q spaces and Hardy-Hausdorff spaces. 相似文献
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In this paper we establish a new bilinear estimate in suitable Bourgain spaces by using a fundamental estimate on dyadic blocks for the Kawahara equation which was obtained by the [k;Z] multiplier norm method of Tao (2001) [2]; then the local well-posedness of the Cauchy problem for a fifth-order shallow water wave equation in with is obtained by the Fourier restriction norm method. And some ill-posedness in with is derived from a general principle of Bejenaru and Tao. 相似文献
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Zhichun Zhai 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(8):2611-2630
Let be the space of solutions to the parabolic equation having finite norm. We characterize nonnegative Radon measures μ on having the property , 1≤p≤q<∞, whenever . Meanwhile, denoting by v(t,x) the solution of the above equation with Cauchy data v0(x), we characterize nonnegative Radon measures μ on satisfying , β∈(0,n), p∈[1,n/β], q∈(0,∞). Moreover, we obtain the decay of v(t,x), an isocapacitary inequality and a trace inequality. 相似文献
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This paper deals with a generalization of the p-Laplacian type boundary value problem
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Bhatia Sumit Kaur 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(8):2368-2382
Let Ω be a bounded domain in RN,N≥2, with C2 boundary. In this work, we study the existence of multiple positive solutions of the following problem: