共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
Mohamed Benrhouma 《Journal of Mathematical Analysis and Applications》2009,358(2):307-2694
In this paper, we study the existence and the uniqueness of positive solution for the sublinear elliptic equation, −Δu+u=p|u|sgn(u)+f in RN, N?3, 0<p<1, f∈L2(RN), f>0 a.e. in RN. We show by applying a minimizing method on the Nehari manifold that this problem has a unique positive solution in H1(RN)∩Lp+1(RN). We study its continuity in the perturbation parameter f at 0. 相似文献
3.
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
4.
Weilin Zou 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(9):3069-3082
This paper deals with a class of degenerate quasilinear elliptic equations of the form −div(a(x,u,∇u)=g−div(f), where a(x,u,∇u) is allowed to be degenerate with the unknown u. We prove existence of bounded solutions under some hypothesis on f and g. Moreover we prove that there exists a renormalized solution in the case where g∈L1(Ω) and f∈(Lp′(Ω))N. 相似文献
5.
Yulian An 《Journal of Mathematical Analysis and Applications》2006,322(2):1071-1082
In this article, we consider uniqueness of positive radial solutions to the elliptic system Δu+a(|x|)f(u,v)=0, Δv+b(|x|)g(u,v)=0, subject to the Dirichlet boundary condition on the open unit ball in RN (N?2). Our uniqueness results applies to, for instance, f(u,v)=uqvp, g(u,v)=upvq, p,q>0, p+q<1 or more general cases. 相似文献
6.
Fabrizio Cuccu Giovanni Porru 《Journal of Mathematical Analysis and Applications》2010,369(1):222-231
We deal with the equations Δpu+f(u)=0 and Δpu+(p−1)g(u)p|∇u|+f(u)=0 in RN, where g(t) is a continuous function in (0,∞), p>1 and f(t) is a smooth function for t>0. Under appropriate conditions on g and f we show that the corresponding equation cannot have nontrivial non-negative entire solutions. 相似文献
7.
Jiangang Cheng 《Journal of Mathematical Analysis and Applications》2006,313(1):322-341
This paper is concerned with the exact number of positive solutions for the boundary value problem ′(|y′|p−2y′)+λf(y)=0 and y(−1)=y(1)=0, where p>1 and λ>0 is a positive parameter. We consider the case in which both f(u) and g(u)=(p−1)f(u)−uf′(u) change sign exactly once from negative to positive on (0,∞). 相似文献
8.
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
9.
Francisco Odair de Paiva Eugenio Massa 《Journal of Mathematical Analysis and Applications》2008,342(1):638-650
We consider the Dirichlet problem for the equation −Δu=λu±f(x,u)+h(x) in a bounded domain, where f has a sublinear growth and h∈L2. We find suitable conditions on f and h in order to have at least two solutions for λ near to an eigenvalue of −Δ. A typical example to which our results apply is when f(x,u) behaves at infinity like a(x)|u|q−2u, with M>a(x)>δ>0, and 1<q<2. 相似文献
10.
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
11.
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
12.
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
13.
Vitali Liskevich I.I. Skrypnik 《Journal of Mathematical Analysis and Applications》2008,338(1):536-544
We study the problem of removability of isolated singularities for a general second-order quasi-linear equation in divergence form −divA(x,u,∇u)+a0(x,u)+g(x,u)=0 in a punctured domain Ω?{0}, where Ω is a domain in Rn, n?3. The model example is the equation −Δpu+gu|u|p−2+u|u|q−1=0, q>p−1>0, p<n. Assuming that the lower-order terms satisfy certain non-linear Kato-type conditions, we prove that for all point singularities of the above equation are removable, thus extending the seminal result of Brezis and Véron. 相似文献
14.
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
15.
Marius Ghergu 《Journal of Mathematical Analysis and Applications》2009,352(1):132-138
We study the degenerate parabolic equation t∂u=a(δ(x))upΔu−g(u) in Ω×(0,∞), where Ω⊂RN (N?1) is a smooth bounded domain, p?1, δ(x)=dist(x,∂Ω) and a is a continuous nondecreasing function such that a(0)=0. Under some suitable assumptions on a and g we prove the existence and the uniqueness of a classical solution and we study its asymptotic behavior as t→∞. 相似文献
16.
Xiaojing Feng Pengcheng Niu Qianqiao Guo 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(4):1119-1131
In this paper, we study the existence and multiplicity of nontrivial solutions for the following second-order Dirichlet nonlinear boundary value problem with odd order derivative: −u″(t)+au′(t)+bu(t)=f(t,u(t)) for all t∈[0,1] with u(0)=u(1)=0, where a,b∈R1, f∈C1([0,1]×R1,R1). By using the Morse theory, we impose certain conditions on f which are able to guarantee that the problem has at least one nontrivial solution, two nontrivial solutions and infinitely many solutions, separately. 相似文献
17.
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
18.
Richard Avery 《Journal of Mathematical Analysis and Applications》2003,277(2):395-404
We apply the Five Functionals Fixed Point Theorem to verify the existence of at least three positive pseudo-symmetric solutions for the three point boundary value problem, (g(u′))′+a(t)f(u)=0, u(0)=0, and u(ν)=u(1), where g(v)=|v|p−2v, with p>1 and ν∈(0,1). 相似文献
19.
By using fixed point theorem, we study the following equation g(u′′(t))+a(t)f(u)=0 subject to boundary conditions, where g(v)=|v|p−2v with p>1; the existence of at least three positive solutions is proved. 相似文献
20.
Mihai Mih?ilescu 《Journal of Mathematical Analysis and Applications》2007,330(1):416-432
We study the boundary value problem −div(log(1+q|∇u|)|∇u|p−2∇u)=f(u) in Ω, u=0 on ∂Ω, where Ω is a bounded domain in RN with smooth boundary. We distinguish the cases where either f(u)=−λ|u|p−2u+|u|r−2u or f(u)=λ|u|p−2u−|u|r−2u, with p, q>1, p+q<min{N,r}, and r<(Np−N+p)/(N−p). In the first case we show the existence of infinitely many weak solutions for any λ>0. In the second case we prove the existence of a nontrivial weak solution if λ is sufficiently large. Our approach relies on adequate variational methods in Orlicz-Sobolev spaces. 相似文献