共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, the fuzzy Basset equation is introduced. This problem is related to the motion of a sphere in a viscous liquid when its parameters are fuzzy numbers. We investigate the existence and uniqueness of solution with converting the problem to a system of fuzzy fractional differential equation, and the solution is also obtained under Caputo generalized Hukuhara differentiability. Some examples show the effectiveness and efficiency our approach. 相似文献
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Let Ω ? 0 be an open bounded domain in R N (N ≥ 3) and $2^* (s) = \tfrac{{2(N - s)}} {{N - 2}}$ , 0 < s < 2. We consider the following elliptic system of two equations in H 0 1 (Ω) × H 0 1 (Ω): $$- \Delta u - t\frac{u} {{\left| x \right|^2 }} = \frac{{2\alpha }} {{\alpha + \beta }}\frac{{\left| u \right|^{\alpha - 2} u\left| v \right|^\beta }} {{\left| x \right|^s }} + \lambda u, - \Delta v - t\frac{v} {{\left| x \right|^2 }} = \frac{{2\beta }} {{\alpha + \beta }}\frac{{\left| u \right|^\alpha \left| v \right|^{\beta - 2} v}} {{\left| x \right|^s }} + \mu v,$$ where λ, µ > 0 and α, β > 1 satisfy α + β = 2*(s). Using the Moser iteration, we prove the asymptotic behavior of solutions at the origin. In addition, by exploiting the Mountain-Pass theorem, we establish the existence of solutions. 相似文献
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Jianfu Yang 《Proceedings of the American Mathematical Society》2004,132(5):1355-1366
We establish an existence result for semilinear elliptic problems with the associated functional not satisfying the Palais-Smale condition. The nonlinearity of our problem does not satisfy the Ambrosetti-Rabinowitz condition.
4.
This article deals with the conditions that ensure the blow-up phenomenon or its absence for solutions of the system ut=△ul up1vq1 and vt=△vm up2vq2 with homogeneous Dirichlet boundary conditions. The results depend crucially on the sign of the difference p2q1-(l-P1)(m-q2), the initial data, and the domainΩ. 相似文献
5.
Existence and regularity of positive solutions of a degenerate elliptic Dirichlet problem of the form in Ω, on , where Ω is a bounded smooth domain in , , are obtained via new embeddings of some weighted Sobolev spaces with singular weights and . It is seen that and admit many singular points in Ω. The main embedding results in this paper provide some generalizations of the well‐known Caffarelli–Kohn–Nirenberg inequality. 相似文献
6.
Wei DONG Jian Tao CHEN 《数学学报(英文版)》2006,22(3):665-670
The goal of this paper is to study the multiplicity result of positive solutions of a class of degenerate elliptic equations. On the basis of the mountain pass theorems and the sub- and supersolutions argument for p-Laplacian operators, under suitable conditions on the nonlinearity f(x, s), we show the following problem:-△pu=λu^α-a(x)u^q in Ω,u│δΩ=0 possesses at least two positive solutions for large λ, where Ω is a bounded open subset of R^N, N ≥ 2, with C^2 boundary, λ is a positive parameter, Ap is the p-Laplacian operator with p 〉 1, α, q are given constants such that p - 1 〈α 〈 q, and a(x) is a continuous positive function in Ω^-. 相似文献
7.
By weakening or dropping the superquadraticity condition (SQC), the existence of positive solutions for a class of elliptic
equations is established. In particular, we deal with the asymptotical linearities as well as the superlinear nonlinearities. 相似文献
8.
Junli Yuan 《Applicable analysis》2013,92(8):1229-1239
Existence of bounded positive solutions of a class of quasi-linear elliptic equation is obtained in exterior domain of R N , N ≥ 1. Firstly, by using fixed point theory, the existence theorem of a class of ordinary differential equation is established. Then, by constructing super-solution and sub-solution, the existence of bounded positive solutions of quasi-linear elliptic equation is given. The results of this article are new and extend previously known results. 相似文献
9.
Let X = (X1, ···, Xm) be an infinitely degenerate system of vector fields. The aim of this paper is to study the existence of infinitely many solutions for the sum of operators X =sum ( ) form j=1 to m Xj Xj. 相似文献
10.
Abstract. The existence of positive radial solutions to the systems of 相似文献
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Zuodong Yang 《Journal of Mathematical Analysis and Applications》2003,288(2):768-783
We show the existence of entire explosive positive radial solutions for quasilinear elliptic systems div(|∇u|m−2∇u)=p(|x|)g(v), div(|∇v|n−2∇v)=q(|x|)f(u) on , where f and g are positive and non-decreasing functions on (0,∞) satisfying the Keller-Osserman condition. 相似文献
13.
Nguyen Thanh Chung Hoang Quoc Toan 《Journal of Mathematical Analysis and Applications》2009,360(2):422-431
This paper deals with the nonexistence and multiplicity of nonnegative, nontrivial solutions to a class of degenerate and singular elliptic systems of the form where Ω is a bounded domain with smooth boundary ∂Ω in , N2, and , , hi (i=1,2) are allowed to have “essential” zeroes at some points in Ω, (Fu,Fv)=F, and λ is a positive parameter. Our proofs rely essentially on the critical point theory tools combined with a variant of the Caffarelli–Kohn–Nirenberg inequality in [P. Caldiroli, R. Musina, On a variational degenerate elliptic problem, NoDEA Nonlinear Differential Equations Appl. 7 (2000) 189–199]. 相似文献
14.
Chuanzhi Bai 《Journal of Applied Analysis & Computation》2016,6(4):1064-1072
In this paper, by using the Morse theory, we obtain the existence of nontrivial weak solutions of quasilinear elliptic systems with Hardy potential. 相似文献
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利用临界点理论中的山路引理,证明一类含退化椭圆算子的Kirchhoff型方程在适当的假设条件下解的存在性,所得结论丰富和发展了已有文献的相关结果. 相似文献
18.
Existence and Multiplicity of solutions for a quasilinear elliptic system on unbounded domains involving nonlinear boundary conditions 下载免费PDF全文
Somayeh Khademloo Ghasem Alizadeh Afrouzi Jiafa Xu 《Journal of Applied Analysis & Computation》2020,10(3):1094-1106
We prove two existence results for the nonlinear elliptic boundary value system involving $p$-Laplacian over an unbounded domain in $R^N$ with noncompact boundary. The proofs are based on variational methods applied to weighted spaces. 相似文献
19.
研究奇异拟线性椭圆型方程{-div(|x|~(-ap)|▽u|~(p-2)▽u) + f(x)|u|~(p-2) = g(x)\u|~(q-2)u + λh(x)|u|~(r-2),x R~N,u(x) 0,x∈ R~N,其中λ0是参数,1pN(N3),1rpgp*=0a(N—p)/p,p*=Np/{N~pd),aa+l,d=a+l-60,权函数f(x),g(x),h(x)满足一定的条件.利用山路引理和Ekeland变分原理证明了问题至少有两个非平凡的弱解. 相似文献
20.
In this paper, using the mountain pass theorem, we give the existence result for nontrivial solutions for a class of asymptotically linear fourth-order elliptic equations. 相似文献