共查询到20条相似文献,搜索用时 812 毫秒
1.
Dongsheng Kang 《Journal of Mathematical Analysis and Applications》2004,299(1):273-284
Let N?3, 2<p<N, 0?s<p and . Via the variational methods and analytic technique, we prove the existence of nontrivial solution to the singular quasilinear problem , for N?p2 and suitable functions f(u). 相似文献
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We study the existence of positive solutions of the m-polyharmonic nonlinear elliptic equation m(−Δ)u+f(⋅,u)=0 in the half-space , n?2 and m?1. Our purpose is to give two existence results for the above equation subject to some boundary conditions, where the nonlinear term f(x,t) satisfies some appropriate conditions related to a certain Kato class of functions . 相似文献
4.
Saroj Kumar Dash 《Journal of Mathematical Analysis and Applications》2008,339(1):98-107
For a symmetric stable process X(t,ω) with index α∈(1,2], f∈Lp[0,2π], p?α, and , we establish that the random Fourier-Stieltjes (RFS) series converges in the mean to the stochastic integral , where fβ is the fractional integral of order β of the function f for . Further it is proved that the RFS series is Abel summable to . Also we define fractional derivative of the sum of order β for an, An(ω) as above and . We have shown that the formal fractional derivative of the series of order β exists in the sense of mean. 相似文献
5.
Sebastián Lorca 《Journal of Mathematical Analysis and Applications》2004,295(1):276-286
We study the existence of positive solutions to the elliptic equation ε2Δu(x,y)−V(y)u(x,y)+f(u(x,y))=0 for (x,y) in an unbounded domain subject to the boundary condition u=0 whenever is nonempty. Our potential V depends only on the y variable and is a bounded or unbounded domain which may coincide with . The positive parameter ε is tending to zero and our solutions uε concentrate along minimum points of the unbounded manifold of critical points of V. 相似文献
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For any numerical function we give sufficient conditions for resolving the controlled extension problem for a closed subset A of a normal space X. Namely, if the functions , and satisfy the equality E(f(a),g(a))=h(a), for every a∈A, then we are interested to find the extensions f? and ? of f and g, respectively, such that , for every x∈X. We generalize earlier results concerning E(u,v)=u·v by using the techniques of selections of paraconvex-valued LSC mappings and soft single-valued mappings. 相似文献
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By Karamata regular varying theory, a perturbed argument and constructing comparison functions, we show the exact asymptotic behaviour of the unique solution near the boundary to a singular Dirichlet problem −Δu=b(x)g(u)+λf(u), u>0, x∈Ω, u|∂Ω=0, which is independent on λf(u), and we also show the existence and uniqueness of solutions to the problem, where Ω is a bounded domain with smooth boundary in RN, λ>0, g∈C1((0,∞),(0,∞)) and there exists γ>1 such that , ∀ξ>0, , the function is decreasing on (0,∞) for some s0>0, and b is nonnegative nontrivial on Ω, which may be vanishing on the boundary. 相似文献
8.
Xianling Fan 《Journal of Mathematical Analysis and Applications》2009,349(2):436-442
Consider the eigenvalue problem : −Δu=λf(x,u) in Ω, u=0 on ∂Ω, where Ω is a bounded smooth domain in RN. Denote by the set of all Carathéodory functions f:Ω×R→R such that for a.e. x∈Ω, f(x,⋅) is Lipschitzian with Lipschitz constant L, f(x,0)=0 and , and denote by (resp. ) the set of λ>0 such that has at least one nonzero classical (resp. weak) solution. Let λ1 be the first eigenvalue for the Laplacian-Dirichlet problem. We prove that and . Our result is a positive answer to Ricceri's conjecture if use f(x,u) instead of f(u) in the conjecture. 相似文献
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Zhijun Zhang 《Journal of Mathematical Analysis and Applications》2005,308(2):532-540
By constructing the comparison functions and the perturbed method, it is showed that any solution u∈C2(Ω) to the semilinear elliptic problems Δu=k(x)g(u), x∈Ω, u|∂Ω=+∞ satisfies , where Ω is a bounded domain with smooth boundary in RN; , −2<σ, c0>0, ; g∈C1[0,∞), g?0 and is increasing on (0,∞), there exists ρ>0 such that , ∀ξ>0, , . 相似文献
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Let be the polynomial whose zeros are the j-invariants of supersingular elliptic curves over . Generalizing a construction of Atkin described in a recent paper by Kaneko and Zagier (Computational Perspectives on Number Theory (Chicago, IL, 1995), AMS/IP 7 (1998) 97-126), we define an inner product on for every . Suppose a system of orthogonal polynomials {Pn,ψ(x)}n=0∞ with respect to exists. We prove that if n is sufficiently large and ψ(x)Pn,ψ(x) is p-integral, then over . Further, we obtain an interpretation of these orthogonal polynomials as a p-adic limit of polynomials associated to p-adic modular forms. 相似文献
12.
V. Raghavendra 《Journal of Mathematical Analysis and Applications》2003,288(1):314-325
In this paper we study the existence of nontrivial solution of the problem −Δpu−(μ/[d(x)]p)|u|p−2u=f(u) in Ω and u=0 on ∂Ω, where is a bounded domain with smooth boundary in Existence is established using mountain-pass lemma and concentration of compactness principle. 相似文献
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Wolfgang Reichel 《Journal of Mathematical Analysis and Applications》2003,287(1):61-74
We study polyharmonic boundary value problems (−Δ)mu=f(u), , with Dirichlet boundary conditions on bounded and unbounded conformally contractible domains in . Such domains can be contracted to a point (bounded case) or to infinity (unbounded case) by one-parameter groups of conformal maps. The class of star-shaped domain is a subclass. The problem has variational structure. This allows us to derive a sufficient condition for uniqueness by studying the interaction of one-parameter transformation groups with the underlying functional . If the transformation group strictly reduces the values of then uniqueness of the critical point of follows. The proof is inspired by E. Noether's theorem on symmetries and conservation laws. Applications of the uniqueness principle are given in Part II of this paper. 相似文献
14.
Liangping Jiang 《Journal of Mathematical Analysis and Applications》2005,301(2):378-383
The classical criterion of asymptotic stability of the zero solution of equations x′=f(t,x) is that there exists a positive definite function V which has infinitesimal upper bound such that is negative definite. In this paper we prove that if is bounded then the condition that is negative definite can be weakened and replaced by that and is negative definite. 相似文献
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In this paper, we prove that a univalent orientation-preserving harmonic mapping defined on the unit disk U with the normalization f(0)=0, , is a typically real mapping, if f(U) is a starlike domain with respect to the origin or f(U) is convex in one direction. 相似文献
16.
Let k be a positive integer with k?2 and let be a family of functions meromorphic on a domain D in , all of whose poles have multiplicity at least 3, and of whose zeros all have multiplicity at least k+1. Let a(z) be a function holomorphic on D, a(z)?0. Suppose that for each , f(k)(z)≠a(z) for z∈D. Then is a normal family on D. 相似文献
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Michela Eleuteri 《Journal of Mathematical Analysis and Applications》2008,344(2):1120-1142
We prove regularity results for minimizers of functionals in the class , where is a fixed function and f is quasiconvex and fulfills a growth condition of the type
L−1|z|p(x)?f(x,ξ,z)?L(1+|z|p(x)), 相似文献
19.
Liangping Jiang 《Journal of Mathematical Analysis and Applications》2007,326(2):1379-1382
The classical criterion of asymptotic stability of the zero solution of equations x′=f(t,x) is that there exists a function V(t,x), a(‖x‖)?V(t,x)?b(‖x‖) for some a,b∈K, such that for some c∈K. In this paper we prove that if f(t,x) is bounded, is uniformly continuous and bounded, then the condition that can be weakened and replaced by and contains no complete trajectory of , t∈[−T,T], where , uniformly for (t,x)∈[−T,T]×BH. 相似文献
20.
In this paper, we show that if is an n-dimensional subspace of L(V) such that every nonzero transformation of has rank greater than or equal to 2n−1 then is algebraically reflexive. If is an n-dimensional subspace of B(H) such that every nonzero transformation of has rank greater than or equal to 2n−1 then is hyperreflexive. We also consider how to construct some new hyperreflexive subspaces. 相似文献