共查询到20条相似文献,搜索用时 505 毫秒
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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:
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Let Ω⊂RN, N?2, be a bounded domain. We consider the following quasilinear problem depending on a real parameter λ>0:
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Jiong Qi Wu 《Journal of Differential Equations》2007,235(2):510-526
Suppose that β?0 is a constant and that is a continuous function with R+:=(0,∞). This paper investigates N-dimensional singular, quasilinear elliptic equations of the form
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We construct positive solutions of the semilinear elliptic problem with Dirichet boundary conditions, in a bounded smooth domain Ω⊂RN(N?4), when the exponent p is supercritical and close enough to and the parameter λ∈R is small enough. As , the solutions have multiple blow up at finitely many points which are the critical points of a function whose definition involves Green's function. Our result extends the result of Del Pino et al. (J. Differential Equations 193(2) (2003) 280) when Ω is a ball and the solutions are radially symmetric. 相似文献
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Zhijun Zhang 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(10):3348-3363
In this paper, we study the boundary behavior of solutions to boundary blow-up elliptic problems , where Ω is a bounded domain with smooth boundary in RN, q>0, , which is positive in Ω and may be vanishing on the boundary and rapidly varying near the boundary, and f is rapidly varying or normalized regularly varying at infinity. 相似文献
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Let Ω be a bounded domain in R2, u+=u if u?0, u+=0 if u<0, u−=u+−u. In this paper we study the existence of solutions to the following problem arising in the study of a simple model of a confined plasma
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Giovanni Anello 《Journal of Differential Equations》2007,234(1):80-90
In this paper we prove that if the potential has a suitable oscillating behavior in any neighborhood of the origin (respectively +∞), then under very mild conditions on the perturbation term g, for every k∈N there exists bk>0 such that
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H. Abels 《Journal of Differential Equations》2007,236(1):29-56
Given a bounded domain Ω⊂Rd and two integro-differential operators L1, L2 of the form we study the fully nonlinear Bellman equation
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Let Ω⊂R4 be a smooth oriented bounded domain, be the Sobolev space, and be the first eigenvalue of the bi-Laplacian operator Δ2. Then for any α: 0?α<λ(Ω), we have
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We prove that if Ω⊆R2 is bounded and R2?Ω satisfies suitable structural assumptions (for example it has a countable number of connected components), then W1,2(Ω) is dense in W1,p(Ω) for every 1?p<2. The main application of this density result is the study of stability under boundary variations for nonlinear Neumann problems of the form
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Mark S. Ashbaugh Fritz Gesztesy Marius Mitrea Gerald Teschl 《Advances in Mathematics》2010,223(4):1372-885
We study spectral properties for HK,Ω, the Krein-von Neumann extension of the perturbed Laplacian −Δ+V defined on , where V is measurable, bounded and nonnegative, in a bounded open set Ω⊂Rn belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class C1,r, r>1/2. In particular, in the aforementioned context we establish the Weyl asymptotic formula
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Markus Biegert 《Journal of Differential Equations》2009,247(7):1949-698
Let Ω⊂RN be a bounded domain and let μ be an admissible measure on ∂Ω. We show in the first part that if Ω has the H1-extension property, then a realization of the Laplace operator with generalized nonlinear Robin boundary conditions, formally given by on ∂Ω, generates a strongly continuous nonlinear submarkovian semigroup SB=(SB(t))t?0 on L2(Ω). We also obtain that this semigroup is ultracontractive in the sense that for every u,v∈Lp(Ω), p?2 and every t>0, one has
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We consider the stationary Gierer-Meinhardt system in a ball of RN:
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Yasuhito Miyamoto 《Journal of Differential Equations》2010,249(8):1853-1870
Let (n?3) be a ball, and let f∈C3. We are concerned with the Neumann problem
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T. Kolokolonikov 《Journal of Differential Equations》2008,245(4):964-993
We consider the stationary Gierer-Meinhardt system in a ball of RN: