共查询到20条相似文献,搜索用时 12 毫秒
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Gleiciane S. Aragão Antônio L. Pereira Marcone C. Pereira 《Mathematical Methods in the Applied Sciences》2012,35(9):1110-1116
In this paper, we investigate the behavior of a family of steady‐state solutions of a nonlinear reaction diffusion equation when some reaction and potential terms are concentrated in a ε‐neighborhood of a portion Γ of the boundary. We assume that this ε‐neighborhood shrinks to Γ as the small parameter ε goes to zero. Also, we suppose the upper boundary of this ε‐strip presents a highly oscillatory behavior. Our main goal here was to show that this family of solutions converges to the solutions of a limit problem, a nonlinear elliptic equation that captures the oscillatory behavior. Indeed, the reaction term and concentrating potential are transformed into a flux condition and a potential on Γ, which depends on the oscillating neighborhood. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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Martin Dindos 《Transactions of the American Mathematical Society》2003,355(4):1365-1399
Extending our recent work for the semilinear elliptic equation on Lipschitz domains, we study a general second-order Dirichlet problem in . We improve our previous results by studying more general nonlinear terms with polynomial (and in some cases exponential) growth in the variable . We also study the case of nonnegative solutions.
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This paper is concerned with exact boundary behavior of large solutions to semilinear elliptic equations △u=b(x)f(u)(C0+|▽u|q),x∈Ω,where Ω is a bounded domain with a smooth boundary in RN,C0≥0,q E [0,2),b∈Clocα(Ω) is positive in but may be vanishing or appropriately singular on the boundary,f∈C[0,∞),f(0)=0,and f is strictly increasing on [0,∞)(or f∈C(R),f(s)> 0,■s∈R,f is strictly increasing on R).We show unified boundary behavior of such solutions to the problem under a new structure condition on f. 相似文献
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Marius Bochniak 《Mathematische Nachrichten》2003,250(1):17-24
The paper is devoted to the study of solutions to linear elliptic boundary value problems in domains depending smoothly on a small perturbation parameter. To this end we transform the boundary value problem onto a fixed reference domain and obtain a problem in a fixed domain but with differential operators depending on the perturbation parameter. Using the Fredholm property of the underlying operator we show the differentiability of the transformed solution under the assumption that the dimension of the kernel does not depend on the perturbation parameter. Furthermore, we obtain an explicit representation for the corresponding derivative. 相似文献
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Positive solutions to sublinear second-order divergence type elliptic equations in cone-like domains
Vitaly Moroz 《Journal of Mathematical Analysis and Applications》2009,352(1):418-426
We study the existence and nonexistence of positive solutions to a sublinear (p<1) second-order divergence type elliptic equation in unbounded cone-like domains CΩ. We prove the existence of the critical exponent
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Tommaso Leonori Alessio Porretta 《Journal of Mathematical Analysis and Applications》2018,457(2):1492-1501
We prove a comparison principle for unbounded weak sub/super solutions of the equation where is a bounded coercive matrix with measurable ingredients, and has a super linear growth and is convex at infinity. We improve earlier results where the convexity of was required to hold globally. 相似文献
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-regularity up to the boundary is proved for solutions of boundary value problems for elliptic equations with discontinuous coefficients in the plane.
where , 2$">, or with the following normal derivative boundary conditions:
where , 2$">, 0$"> and is the unit outward normal to the boundary .
In particular, we deal with the Dirichlet boundary condition
where , 2$">, or with the following normal derivative boundary conditions:
where , 2$">, 0$"> and is the unit outward normal to the boundary .
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闻国椿 《数学物理学报(B辑英文版)》2007,27(3):663-672
The present article deals with some boundary value problems for nonlinear elliptic equations with degenerate rank 0 including the oblique derivative problem.Firstly the formulation and estimates of solutions of the oblique derivative problem are given, and then by the above estimates and the method of parameter extension,the existence of solutions of the above problem is proved.In this article,the complex analytic method is used,namely the corresponding problem for degenerate elliptic complex equations of first order is firstly discussed,afterwards the above problem for the degenerate elliptic equations of second order is solved. 相似文献
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For n≥3 and p>1, the elliptic equation Δu+K(x)up+μf(x)=0 in possesses a continuum of positive entire solutions, provided that (i) locally Hölder continuous functions K and f vanish rapidly, for instance, K(x),f(x)=O(|x|l) near ∞ for some l<−2 and (ii) μ≥0 is sufficiently small. Especially, in the radial case with K(x)=k(|x|) and f(x)=g(|x|) for some appropriate functions k,g on [0,∞), there exist two intervals Iμ,1, Iμ,2 such that for each α∈Iμ,1 the equation has a positive entire solution uα with uα(0)=α which converges to l∈Iμ,2 at ∞, and uα1<uα2 for any α1<α2 in Iμ,1. Moreover, the map α to l is one-to-one and onto from Iμ,1 to Iμ,2. If K≥0, each solution regarded as a steady state for the corresponding parabolic equation is stable in the uniform norm; moreover, in the radial case the solutions are also weakly asymptotically stable in the weighted uniform norm with weight function |x|n−2. 相似文献
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Olivier Guibé Anna Mercaldo 《Transactions of the American Mathematical Society》2008,360(2):643-669
In this paper we prove the existence of a renormalized solution to a class of nonlinear elliptic problems whose prototype is
where is a bounded open subset of , , is the so-called Laplace operator, , is a Radon measure with bounded variation on , , , and and belong to the Lorentz spaces , , and , respectively. In particular we prove the existence under the assumptions that , belongs to the Lorentz space , , and is small enough.
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We obtain a global estimate for the weak solution to an elliptic partial differential equation of -Laplacian type with BMO coefficients in a Lipschitz domain with small Lipschitz constant.
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