共查询到20条相似文献,搜索用时 93 毫秒
1.
Moshe Sniedovich 《Operations Research Letters》1984,3(5):271-273
It is shown that minimization problems involving objective functions of the form g(x) + ?(u(x)) where ? is concave, can be solved by means of proxy problems, the objective function of which is of the form g(x)+λu(x). 相似文献
2.
Moshe Sniedovich 《Operations Research Letters》1985,4(1):19-21
This paper presents the essentials of a method designed to solve optimization problems whose objective functions are of the form g(x)+ ψ(u(x)), where ψ is differentiable and either concave or convex. It is shown that solutions to such problems can be obtained through the solutions of the Lagrangian problem whose objective function is of the form g(x)+ λu(x). 相似文献
3.
Marius Ghergu 《Journal of Mathematical Analysis and Applications》2007,333(1):265-273
We are concerned with singular elliptic equations of the form −Δu=p(x)(g(u)+f(u)+a|∇u|) in RN (N?3), where p is a positive weight and 0<a<1. Under the hypothesis that f is a nondecreasing function with sublinear growth and g is decreasing and unbounded around the origin, we establish the existence of a ground state solution vanishing at infinity. Our arguments rely essentially on the maximum principle. 相似文献
4.
Meiqiang Feng Xuemei Zhang Weigao Ge 《Journal of Applied Mathematics and Computing》2010,33(1-2):437-448
In this paper, the exact number of pseudo-symmetric positive solutions is obtained for a class of three-point boundary value problems with one-dimensional p-Laplacian. The interesting point is that the nonlinearity f is general form: f(u)=λ g(u)+h(u). Meanwhile, some properties of the solutions are given in details. The arguments are based upon a quadrature method. 相似文献
5.
Meiqiang Feng Xuemei Zhang Weigao Ge 《Journal of Mathematical Analysis and Applications》2008,338(2):784-792
In this paper, exact number of solutions are obtained for the one-dimensional p-Laplacian in a class of two-point boundary value problems. The interesting point is that the nonlinearity f is general form: f(u)=λg(u)+h(u). Meanwhile, some properties of the solutions are given in details. The arguments are based upon a quadrature method. 相似文献
6.
Lazhar Bougoffa 《Applied mathematics and computation》2010,216(2):689-8913
The Abel equation of the second kind
[g0(x)+g1(x)u]u′=f0(x)+f1(x)u+f2(x)u2 相似文献
7.
Smaïl Djebali 《Journal of Mathematical Analysis and Applications》2009,353(1):215-672
This paper is devoted to the existence and properties of solutions of the following class of nonlinear elliptic differential equations Δu(x)+f(x,u(x))+g(‖x‖)x⋅∇u(x)=0, x∈Rn, ‖x‖>R. We prove existence of positive solutions vanishing at positive infinity. Our approach is based on the subsolution and supersolution method. The nonlinearity f covers both sublinear and superlinear cases and does not necessarily satisfy f(x,0)≡0. The asymptotic behavior of solutions is also described. 相似文献
8.
The functional equationf(x,y)+g(x)h(y)F(u/1?x,ν/1?y)=f(u,ν)+g(u)h(ν)F(x/1?u,y/1?ν) ... (1) forx, y, u, ν ∈ [0, 1) andx+u,y+ν ∈ [0,1) whereg andh satisfy the functional equationφ (x+y?xy)=φ(x)φ(y)... (2) has been solved for some non-constant solution of (2) in [0, 1] withφ (0)=1,φ(1)=0 and the solution is used in characterising some measures of information. 相似文献
9.
D. Denny 《Journal of Mathematical Analysis and Applications》2011,380(2):653-668
The purpose of this paper is to prove the existence of a unique classical solution u(x) to the quasilinear elliptic equation −∇⋅(a(u)∇u)+v⋅∇u=f, where u(x0)=u0 at x0∈Ω and where n⋅∇u=g on the boundary ∂Ω. We prove that if the functions a, f, v, g satisfy certain conditions, then a unique classical solution u(x) exists. Applications include stationary heat/diffusion problems with convection and with a source/sink, where the value of the solution is known at a spatial location x0∈Ω, and where n⋅∇u is known on the boundary. 相似文献
10.
Jorge García-Melián 《Journal of Differential Equations》2006,223(1):208-227
In this paper, we use for the first time linearization techniques to deal with boundary blow-up elliptic problems. After introducing a convenient functional setting, we show that the problem Δu=λa(x)up+g(x,u) in Ω, with u=+∞ on ∂Ω, has a unique positive solution for large enough λ, and determine its asymptotic behavior as λ→+∞. Here p>1, a(x) is a continuous function which can be singular near ∂Ω and g(x,u) is a perturbation term with potential growth near zero and infinity. We also consider more general problems, obtained by replacing up by eu or a “logistic type” function f(u). 相似文献
11.
Kaouther Ammar 《Journal of Differential Equations》2007,234(1):1-25
We consider a general class of degenerate elliptic problems of the form Au+g(x,u,Du)=f, where A is a Leray-Lions operator from a weighted Sobolev space into its dual. We assume that g(x,s,ξ) is a Caratheodory function verifying a sign condition and a growth condition on ξ. Existence of renormalized solutions is established in the L1-setting. 相似文献
12.
The authors discuss the quasilinear parabolic equation ut=∇⋅(g(u)∇u)+h(u,∇u)+f(u) with u|∂Ω=0, u(x,0)=?(x). If f, g and h are polynomials with proper degrees and proper coefficients, they show that the blowup property only depends on the first eigenvalue of −Δ in Ω with Dirichlet boundary condition. For a special case, they obtain a sharp result. 相似文献
13.
Alemdar Hasanov Ali Demir Arzu Erdem 《Journal of Mathematical Analysis and Applications》2007,335(2):1434-1451
This article presents a mathematical analysis of input-output mappings in inverse coefficient and source problems for the linear parabolic equation ut=(kx(x)ux)+F(x,t), (x,t)∈ΩT:=(0,1)×(0,T]. The most experimentally feasible boundary measured data, the Neumann output (flux) data f(t):=−k(0)ux(0,t), is used at the boundary x=0. For each inverse problems structure of the input-output mappings is analyzed based on maximum principle and corresponding adjoint problems. Derived integral identities between the solutions of forward problems and corresponding adjoint problems, permit one to prove the monotonicity and invertibility of the input-output mappings. Some numerical applications are presented. 相似文献
14.
Marius Ghergu 《Journal of Differential Equations》2003,195(2):520-536
We establish several existence and nonexistence results for the boundary value problem −Δu+K(x)g(u)=λf(x,u)+μh(x) in Ω, u=0 on ∂Ω, where Ω is a smooth bounded domain in , λ and μ are positive parameters, h is a positive function, while f has a sublinear growth. The main feature of this paper is that the nonlinearity g is assumed to be unbounded around the origin. Our analysis shows the importance of the role played by the decay rate of g combined with the signs of the extremal values of the potential K(x) on . The proofs are based on various techniques related to the maximum principle for elliptic equations. 相似文献
15.
Louis Dupaigne 《Journal de Mathématiques Pures et Appliquées》2007,87(6):563-581
We are concerned with singular elliptic problems of the form −Δu±p(d(x))g(u)=λf(x,u)+μa|∇u| in Ω, where Ω is a smooth bounded domain in RN, d(x)=dist(x,∂Ω), λ>0, μ∈R, 0<a?2, and f is a nondecreasing function. We assume that p(d(x)) is a positive weight with possible singular behavior on the boundary of Ω and that the nonlinearity g is unbounded around the origin. Taking into account the competition between the anisotropic potential p(d(x)), the convection term a|∇u|, and the singular nonlinearity g, we establish various existence and nonexistence results. 相似文献
16.
Aubrey Truman 《Journal of Functional Analysis》2006,238(2):612-635
In this paper we study the initial problem for a stochastic nonlinear equation arising from 1D integro-differential scalar conservation laws. The equation is driven by Lévy space-time white noise in the following form:
(t∂−A)u+x∂q(u)=f(u)+g(u)Ft,x 相似文献
17.
Marius Ghergu 《Journal of Mathematical Analysis and Applications》2005,311(2):635-646
We establish several results related to existence, nonexistence or bifurcation of positive solutions for the boundary value problem −Δu+K(x)g(u)+a|∇u|=λf(x,u) in Ω, u=0 on ∂Ω, where Ω⊂RN(N?2) is a smooth bounded domain, 0<a?2, λ is a positive parameter, and f is smooth and has a sublinear growth. The main feature of this paper consists in the presence of the singular nonlinearity g combined with the convection term a|∇u|. Our approach takes into account both the sign of the potential K and the decay rate around the origin of the singular nonlinearity g. The proofs are based on various techniques related to the maximum principle for elliptic equations. 相似文献
18.
José L. López Ester Pérez Sinusía 《Journal of Mathematical Analysis and Applications》2007,328(2):931-945
We consider three singularly perturbed convection-diffusion problems defined in three-dimensional domains: (i) a parabolic problem −?(uxx+uyy)+ut+v1ux+v2uy=0 in an octant, (ii) an elliptic problem −?(uxx+uyy+uzz)+v1ux+v2uy+v3uz=0 in an octant and (iii) the same elliptic problem in a half-space. We consider for all of these problems discontinuous boundary conditions at certain regions of the boundaries of the domains. For each problem, an asymptotic approximation of the solution is obtained from an integral representation when the singular parameter ?→0+. The solution is approximated by a product of two error functions, and this approximation characterizes the effect of the discontinuities on the small ?− behaviour of the solution and its derivatives in the boundary layers or the internal layers. 相似文献
19.
Ezequiel R. Barbosa Marcos Montenegro 《Journal of Mathematical Analysis and Applications》2008,344(2):699-702
Let (M,g) be a 4-dimensional compact Riemannian manifold and let a,f be positive smooth functions on M. In this note, we prove that the problem Δgu+a(x)u=f(x)u3 always admits a positive solution, up to a conformal deformation of g. This leads to a geometric obstruction result for the prescribed scalar curvature problem. 相似文献
20.
Zhifei Zhang 《Journal of Mathematical Analysis and Applications》2010,363(2):549-558
We discuss the existence of periodic solutions to the wave equation with variable coefficients utt−div(A(x)∇u)+ρ(x,ut)=f(x,t) with Dirichlet boundary condition. Here ρ(x,v) is a function like ρ(x,v)=a(x)g(v) with g′(v)?0 where a(x) is nonnegative, being positive only in a neighborhood of a part of the domain. 相似文献