共查询到20条相似文献,搜索用时 0 毫秒
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This paper deals with the second term asymptotic behavior of large solutions to the problems Δu=b(x)f(u), x∈Ω, subject to the singular boundary condition u(x)=∞, x∈∂Ω, where Ω is a smooth bounded domain in RN, and b(x) is a non-negative weight function. The absorption term f is regularly varying at infinite with index ρ>1 (that is limu→∞f(ξu)/f(u)=ξρ for every ξ>0) and the mapping f(u)/u is increasing on (0,+∞). Our analysis relies on the Karamata regular variation theory. 相似文献
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Florica-Corina Cî rstea Vicentiu Radulescu 《Transactions of the American Mathematical Society》2007,359(7):3275-3286
We establish the uniqueness of the positive solution for equations of the form in , . The special feature is to consider nonlinearities whose variation at infinity is not regular (e.g., , , , , , , or ) and functions in vanishing on . The main innovation consists of using Karamata's theory not only in the statement/proof of the main result but also to link the nonregular variation of at infinity with the blow-up rate of the solution near .
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By Karamata regular variation theory, a perturbation method and constructing comparison functions, we show the exact asymptotic behavior of large solutions to the semilinear elliptic equations with convection terms
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Qing Miao 《Applicable analysis》2013,92(12):1893-1905
For a given bounded domain Ω in R N with smooth boundary ?Ω, we give sufficient conditions on f so that the m-Laplacian equation △ m u = f(x, u, ?u) admits a boundary blow-up solution u ∈ W 1,p (Ω). Our main results are new and extend the results in J.V. Concalves and Angelo Roncalli [Boundary blow-up solutions for a class of elliptic equations on a bounded domain, Appl. Math. Comput. 182 (2006), pp. 13–23]. Our approach employs the method of lower–upper solution theorem, fixed point theory and weak comparison principle. 相似文献
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Shuibo Huang Qiaoyu Tian Shengzhi Zhang Jinhua Xi Zheng-en Fan 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(11):3489-3501
In this paper, combining the method of lower and upper solutions with the localization method, we establish the boundary blow-up rate of the large positive solutions to the singular boundary value problem
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By the Karamata regular variation theory and the method of lower and upper solutions, we establish the asymptotic behavior of boundary blow-up solutions of the quasilinear elliptic equation div(|u|p−2u)=b(x)f(u) in a bounded ΩRN subject to the singular boundary condition u(x)=∞, where the weight b(x) is non-negative and non-trivial in Ω, which may be vanishing on the boundary or go to unbounded, the nonlinear term f is a Γ-varying function at infinity, whose variation at infinity is not regular. 相似文献
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We consider the elliptic system Δu=upvq, Δv=urvs in Ω, where p,s>1, q,r>0, and Ω⊂RN is a smooth bounded domain, subject to different types of Dirichlet boundary conditions: (F) u=λ, v=μ, (I) u=v=+∞ and (SF) u=+∞, v=μ on ∂Ω, where λ,μ>0. Under several hypotheses on the parameters p,q,r,s, we show existence and nonexistence of positive solutions, uniqueness and nonuniqueness. We further provide the exact asymptotic behaviour of the solutions and their normal derivatives near ∂Ω. Some more general related problems are also studied. 相似文献
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Jorge García-Melin 《Journal of Mathematical Analysis and Applications》2009,360(2):530-536
In this paper we prove the uniqueness of the positive solution for the boundary blow-up problem where Ω is a C2 bounded domain in , under the hypotheses that f(t) is nondecreasing in t>0 and f(t)/tp is increasing for large t and some p>1. We also consider the uniqueness of a related problem when the equation includes a nonnegative weight a(x). 相似文献
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Wei Dong 《Journal of Mathematical Analysis and Applications》2004,290(2):469-480
In this paper, we consider positive solutions of the logistic type p-Laplacian equation −Δpu=a(x)|u|p−2u−b(x)|u|q−1u, xRN (N2). We show that under rather general conditions on a(x) and b(x) for large |x|, the behavior of the positive solutions for large |x| can be determined. This is then used to show that there is a unique positive solution. Our results improve the corresponding ones in J. London Math. Soc. (2) 64 (2001) 107–124 and J. Anal. Math., in press. 相似文献
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In this paper, we obtain a blow-up criterion for classical solutions to the 3-D compressible Navier-Stokes equations just in terms of the gradient of the velocity, analogous to the Beal-Kato-Majda criterion for the ideal incompressible flow. In addition, the initial vacuum is allowed in our case. 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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Jorge García-Melián 《Journal of Functional Analysis》2011,261(7):1775-3328
In this paper we consider the elliptic boundary blow-up problem
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Dušan Repovš 《Applied mathematics and computation》2011,218(8):4414-4422
We are concerned with the qualitative analysis of positive singular solutions with blow-up boundary for a class of logistic-type equations with slow diffusion and variable potential. We establish the exact blow-up rate of solutions near the boundary in terms of Karamata regular variation theory. This enables us to deduce the uniqueness of the singular solution. 相似文献
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Jorge García-Melián 《Journal of Differential Equations》2006,223(1):208-227
In this paper, we use for the first time linearization techniques to deal with boundary blow-up elliptic problems. After introducing a convenient functional setting, we show that the problem Δu=λa(x)up+g(x,u) in Ω, with u=+∞ on ∂Ω, has a unique positive solution for large enough λ, and determine its asymptotic behavior as λ→+∞. Here p>1, a(x) is a continuous function which can be singular near ∂Ω and g(x,u) is a perturbation term with potential growth near zero and infinity. We also consider more general problems, obtained by replacing up by eu or a “logistic type” function f(u). 相似文献