共查询到20条相似文献,搜索用时 0 毫秒
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Massimo Grossi 《Journal of Functional Analysis》2008,254(12):2995-3036
Let us consider the problem
(0.1) 相似文献
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We consider the boundary value problem Δu+up=0 in a bounded, smooth domain Ω in R2 with homogeneous Dirichlet boundary condition and p a large exponent. We find topological conditions on Ω which ensure the existence of a positive solution up concentrating at exactly m points as p→∞. In particular, for a nonsimply connected domain such a solution exists for any given m?1. 相似文献
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In this paper, we study the effect of domain shape on the number of 2-nodal solutions for the semilinear elliptic equation involving non-odd nonlinearities. We prove that a semilinear elliptic equation in an m-bump domain (possibly unbounded) has m2 2-nodal solutions and we can find a least energy nodal solution in those solutions. Furthermore, we can describe the bump location of these solutions. 相似文献
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On the ball |x| ≤ 1 of R
m
, m ≥ 2, a radial variational problem, related to a priori estimates for solutions to extremal elliptic equations with fixed
ellipticity constant α
is investigated. Such a problem has been studied and solved [see Manselli Ann. Mat. Pura Appl. (IV), t. LXXXIX:31–54, 1971]
in L
p
spaces, with p ≤ m. In this paper, we assume p > m and we prove the existence of a positive number α
0 = α
0(p,m) such that if there exists a smooth function maximizing the problem, whose representation is explicitly determined as in Manselli [Ann.
Mat. Pura Appl. (IV), t. LXXXIX:31–54, 1971] This fact is no longer true if 0 < α < α
0.
相似文献
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Juan Dávila Marcelo Montenegro 《Journal of Mathematical Analysis and Applications》2009,352(1):360-379
For the equation
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Johnny Henderson H. B. Thompson 《Proceedings of the American Mathematical Society》2000,128(8):2373-2379
For the second order boundary value problem, , , , where growth conditions are imposed on which yield the existence of at least three symmetric positive solutions.
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We consider the following boundary value problem
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There has been a long-standing question of whether certain mesh restrictions are required for a maximum condition to hold for the discrete equations arising from a finite element approximation of an elliptic problem. This is related to knowing whether the discrete Green's function is positive for triangular meshes allowing sufficiently good approximation of functions. We study this question for the Poisson problem in two dimensions discretized via the Galerkin method with continuous piecewise linears. We give examples which show that in general the answer is negative, and furthermore we extend the number of cases where it is known to be positive. Our techniques utilize some new results about discrete Green's functions that are of independent interest.
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Patrick Winkert 《Journal of Mathematical Analysis and Applications》2011,377(1):121-134
The main goal of this paper is to present multiple solution results for elliptic inclusions of Clarke's gradient type under nonlinear Neumann boundary conditions involving the p-Laplacian and set-valued nonlinearities. To be more precise, we study the inclusion
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Aleksandra Orpel 《Journal of Mathematical Analysis and Applications》2004,299(2):690-702
The aim of this paper is to answer the question, when a certain BVP of elliptic type possesses positive radial solutions. We develop duality and variational principles for this problem. Our approach enables the approximation of solutions and gives a measure of a duality gap between primal and dual functional for minimizing sequences. 相似文献
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In this paper we are concerned with a semilinear elliptic Dirichlet problem with jumping nonlinearity and, using a completely variational method, we show that the number of solutions may be arbitrarily large provided the number of jumped eigenvalues is large enough. In order to prove this fact, we show that for every positive integer k, when a suitable parameter is large enough, there exists a solution which presents k peaks. Under the assumptions we consider in this paper, new (unexpected) phenomena are observed in the study of this problem and new methods are required to construct the k-peaks solutions and describe their asymptotic behavior (weak limits of the rescaled solutions, localization of the concentration points of the peaks, asymptotic profile of the rescaled peaks, etc.). 相似文献