共查询到20条相似文献,搜索用时 171 毫秒
1.
Smail Djebali 《Journal of Mathematical Analysis and Applications》2007,333(2):863-870
In this note we investigate the existence of positive solutions vanishing at +∞ to the elliptic equation Δu+f(x,u)+g(|x|)x⋅∇u=0, |x|>A>0, in Rn (n?3) under mild restrictions on the functions f, g. 相似文献
2.
Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations 总被引:1,自引:0,他引:1
In this paper, we investigate the existence of positive solutions for the singular fractional boundary value problem: Dαu(t)+f(t,u(t),Dμu(t))=0, u(0)=u(1)=0, where 1<α<2, 0<μ?α−1, Dα is the standard Riemann-Liouville fractional derivative, f is a positive Carathéodory function and f(t,x,y) is singular at x=0. By means of a fixed point theorem on a cone, the existence of positive solutions is obtained. The proofs are based on regularization and sequential techniques. 相似文献
3.
We study the nonlinear problem −Δu+V(x)=f(x,u), x∈RN, lim|x|→∞u(x)=0, where the Schrödinger operator −Δ+V is semibounded and the nonlinearity f is linearly bounded. We establish compactness of Palais-Smale sequences and Cerami sequences for the associated energy functional under general spectral-theoretic assumptions. Applying these results, we obtain existence of three nontrivial solutions if the energy functional has a mountain-pass geometry. 相似文献
4.
《Journal de Mathématiques Pures et Appliquées》2002,81(9):827-846
We consider the system Δu=p(x)g(v), Δv=q(x)f(u) in , where f,g are positive and non-decreasing functions on (0,∞) satisfying the Keller–Osserman condition and we establish the existence of positive solutions that blow-up at infinity. 相似文献
5.
In this paper, we study the existence of infinitely many nontrivial solutions for a class of semilinear Schrödinger equations −Δu+V(x)u=f(x,u), x∈RN, where the primitive of the nonlinearity f is of superquadratic growth near infinity in u and the potential V is allowed to be sign-changing. 相似文献
6.
C.A. Santos 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(12):6038-6043
We establish a result concerning the existence of entire, positive, classical and bounded solutions which converge to zero at infinity for the semi-linear equation −Δu=λf(x,u),x∈RN, where f:RN×(0,∞)→[0,∞) is a suitable function and λ>0 is a real parameter. This result completes the principal theorem of A. Mohammed [A. Mohammed, Ground state solutions for singular semi-linear elliptic equations, Nonlinear Analysis (2008) doi:10.1016/j.na.2008.11.080] mainly because his result does not address the super-linear terms at infinity. Penalty arguments, lower-upper solutions and an approximation procedure will be used. 相似文献
7.
Miguel Ramos 《Journal of Mathematical Analysis and Applications》2009,352(1):246-258
We study the existence, multiplicity and shape of positive solutions of the system −ε2Δu+V(x)u=K(x)g(v), −ε2Δv+V(x)v=H(x)f(u) in RN, as ε→0. The functions f and g are power-like nonlinearities with superlinear and subcritical growth at infinity, and V, H, K are positive and locally Hölder continuous. 相似文献
8.
Xinfu Chen 《Journal of Differential Equations》2005,212(1):62-84
We consider entire solutions of ut=uxx-f(u), i.e. solutions that exist for all (x,t)∈R2, where f(0)=f(1)=0<f′(0). In particular, we are interested in the entire solutions which behave as two opposite wave fronts of positive speed(s) approaching each other from both sides of the x-axis and then annihilating in a finite time. In the case f′(1)>0, we show that such entire solution exists and is unique up to space-time translations. In the case f′(1)<0, we derive two families of such entire solutions. In the first family, one cannot be any space-time translation of the other. Yet all entire solutions in the second family only differ by a space-time translation. 相似文献
9.
We prove the existence of nontrivial solutions for the Schrödinger equation −Δu+V(x)u=aγ(x)f(u) in RN, where f is superlinear and subcritical at zero and infinity respectively, V is periodic and a(x) changes sign. 相似文献
10.
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
11.
Hongtao Xue 《Journal of Mathematical Analysis and Applications》2011,384(2):439-443
By a sub-supersolution method and a perturbed argument, we improve the earlier results concerning the existence of ground state solutions to a semilinear elliptic problem −Δu+p(x)q|∇u|=f(x,u), u>0, x∈RN, , where q∈(1,2], for some α∈(0,1), p(x)?0, ∀x∈RN, and f:RN×(0,∞)→[0,∞) is a locally Hölder continuous function which may be singular at zero. 相似文献
12.
We study the nonlinear parabolic equation , in Rn×(0,∞) with boundary condition u(x,0)=u0(x), not necessarily bounded function. The nonlinearity φ((x,t),u) is required to satisfy some conditions related to the parabolic Kato class P∞(Rn) while allowing existence of positive solutions of the equation and continuity of such solutions. Our approach is based on potential theory tools. 相似文献
13.
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
14.
In this paper, we study the existence of multiple positive solutions to some Hamiltonian elliptic systems −Δv=λu+up+εf(x), −Δu=μv+vq+δg(x) in Ω;u,v>0 in Ω; u=v=0 on ∂Ω, where Ω is a bounded domain in RN (N?3); 0?f, g∈L∞(Ω); 1/(p+1)+1/(q+1)=(N−2)/N, p,q>1; λ,μ>0. Using sub- and supersolution method and based on an adaptation of the dual variational approach, we prove the existence of at least two nontrivial positive solutions for all λ,μ∈(0,λ1) and ε,δ∈(0,δ0), where λ1 is the first eigenvalue of the Laplace operator −Δ with zero Dirichlet boundary conditions and δ0 is a positive number. 相似文献
15.
Svatoslav Staněk 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(12):e153
The paper discusses the existence of positive and dead core solutions of the singular differential equation (?(u″))′=λf(t,u,u′,u″) satisfying the boundary conditions u(0)=A, u(T)=A, min{u(t):t∈[0,T]}=0. Here λ is a nonnegative parameter, A is a positive constant and the Carathéodory function f(t,x,y,z) is singular at the value 0 of its space variable y. 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.
This paper deals with the second term asymptotic behavior of large solutions to the problems Δu=b(x)f(u), x∈Ω, subject to the singular boundary condition u(x)=∞, x∈∂Ω, where Ω is a smooth bounded domain in RN, and b(x) is a non-negative weight function. The absorption term f is regularly varying at infinite with index ρ>1 (that is limu→∞f(ξu)/f(u)=ξρ for every ξ>0) and the mapping f(u)/u is increasing on (0,+∞). Our analysis relies on the Karamata regular variation theory. 相似文献
18.
We establish that the elliptic equation Δu+K(x)up+μf(x)=0 in Rn has infinitely many positive entire solutions for small μ?0 under suitable conditions on K, p, and f. 相似文献
19.
Yacheng Liu 《Journal of Mathematical Analysis and Applications》2008,338(2):1169-1187
In this paper we study Cauchy problem of generalized double dispersion equations utt−uxx−uxxtt+uxxxx=f(u)xx, where f(u)=p|u|, p>1 or u2k, . By introducing a family of potential wells we not only get a threshold result of global existence and nonexistence of solutions, but also obtain the invariance of some sets and vacuum isolating of solutions. In addition, the global existence and finite time blow up of solutions for problem with critical initial conditions E(0)=d, I(u0)?0 or I(u0)<0 are proved. 相似文献
20.
Shuibo Huang Qiaoyu Tian Shengzhi Zhang Jinhua Xi 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(6):2342-2350
We investigate second-term asymptotic behavior of boundary blow-up solutions to the problems Δu=b(x)f(u), x∈Ω, subject to the singular boundary condition u(x)=∞, in a bounded smooth domain Ω⊂RN. b(x) is a non-negative weight function. The nonlinearly f is regularly varying at infinity with index ρ>1 (that is limu→∞f(ξu)/f(u)=ξρ for every ξ>0) and the mapping f(u)/u is increasing on (0,+∞). The main results show how the mean curvature of the boundary ∂Ω appears in the asymptotic expansion of the solution u(x). Our analysis relies on suitable upper and lower solutions and the Karamata regular variation theory. 相似文献