共查询到20条相似文献,搜索用时 31 毫秒
1.
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
2.
We show the existence and nonexistence of entire positive solutions for semilinear elliptic system with gradient term Δu+|∇u|=p(|x|)f(u,v), Δv+|∇v|=q(|x|)g(u,v) on RN, N?3, provided that nonlinearities f and g are positive and continuous, the potentials p and q are continuous, c-positive and satisfy appropriate growth conditions at infinity. We find that entire large positive solutions fail to exist if f and g are sublinear and p and q have fast decay at infinity, while if f and g satisfy some growth conditions at infinity, and p, q are of slow decay or fast decay at infinity, then the system has infinitely many entire solutions, which are large or bounded. 相似文献
3.
Hong Li 《Journal of Mathematical Analysis and Applications》2010,365(1):338-333
Under the simple conditions on f and g, we show that entire positive radial solutions exist for the semilinear elliptic system Δu=p(|x|)f(v), Δv=q(|x|)g(u), x∈RN, N?3, where the functions are continuous. 相似文献
4.
Alan V. Lair 《Journal of Mathematical Analysis and Applications》2010,365(1):103-449
We prove that the elliptic system Δu=p(|x|)vα, Δv=q(|x|)uβ on Rn (n?3) where 0<α?1, 0<β?1, and p and q are nonnegative continuous functions has a nonnegative entire radial solution satisfying lim|x|→∞u(x)=lim|x|→∞v(x)=∞ if and only if the functions p and q satisfy
5.
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
6.
Jesse D. Peterson Aihua W. Wood 《Journal of Mathematical Analysis and Applications》2011,384(2):284-292
We present the existence of entire large positive radial solutions for the non-monotonic system Δu=p(|x|)g(v), Δv=q(|x|)f(u) on Rn where n?3. The functions f and g satisfy a Keller-Osserman type condition while nonnegative functions p and q are required to satisfy the decay conditions and . Further, p and q are such that min(p,q) does not have compact support. 相似文献
7.
《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
8.
In this paper we consider radially symmetric solutions of the nonlinear Dirichlet problem Δu+f(|x|,u)=0 in Ω, where Ω is a ball in RN, N?3 and f satisfies some appropriate assumptions. We prove existence of radially symmetric solutions with k prescribed number of zeros. Moreover, when f(|x|,u)=K(|x|)|u|p−1u, using the uniqueness result due to Tanaka (2008) [21], we verify that these solutions are non-degenerate and we prove that their radial Morse index is exactly k. 相似文献
9.
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
10.
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
11.
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
12.
Ahmed Hamydy 《Journal of Mathematical Analysis and Applications》2010,371(2):534-169
Assume that Ω is a bounded domain in RN (N?3) with smooth boundary ∂Ω. In this work, we study existence and uniqueness of blow-up solutions for the problem −Δp(u)+c(x)|∇u|p−1+F(x,u)=0 in Ω, where 2?p. Under some conditions related to the function F, we give a sufficient condition for existence and nonexistence of nonnegative blow-up solutions. We study also the uniqueness of these solutions. 相似文献
13.
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
14.
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
15.
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
16.
Goro Akagi 《Journal of Differential Equations》2007,241(2):359-385
The existence of local (in time) solutions of the initial-boundary value problem for the following degenerate parabolic equation: ut(x,t)−Δpu(x,t)−|u|q−2u(x,t)=f(x,t), (x,t)∈Ω×(0,T), where 2?p<q<+∞, Ω is a bounded domain in RN, is given and Δp denotes the so-called p-Laplacian defined by Δpu:=∇⋅(|∇u|p−2∇u), with initial data u0∈Lr(Ω) is proved under r>N(q−p)/p without imposing any smallness on u0 and f. To this end, the above problem is reduced into the Cauchy problem for an evolution equation governed by the difference of two subdifferential operators in a reflexive Banach space, and the theory of subdifferential operators and potential well method are employed to establish energy estimates. Particularly, Lr-estimates of solutions play a crucial role to construct a time-local solution and reveal the dependence of the time interval [0,T0] in which the problem admits a solution. More precisely, T0 depends only on Lr|u0| and f. 相似文献
17.
Luciano Mari 《Journal of Functional Analysis》2010,258(2):665-2670
In this paper we obtain essentially sharp generalized Keller-Osserman conditions for wide classes of differential inequalities of the form Lu?b(x)f(u)?(|∇u|) and Lu?b(x)f(u)?(|∇u|)−g(u)h(|∇u|) on weighted Riemannian manifolds, where L is a non-linear diffusion-type operator. Prototypical examples of these operators are the p-Laplacian and the mean curvature operator. The geometry of the underlying manifold is reflected, via bounds for the modified Bakry-Emery Ricci curvature, by growth conditions for the functions b and ?. A weak maximum principle which extends and improves previous results valid for the φ-Laplacian is also obtained. Geometric comparison results, valid even in the case of integral bounds for the modified Bakry-Emery Ricci tensor, are presented. 相似文献
18.
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
19.
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
20.
For n≥3 and p>1, the elliptic equation Δu+K(x)up+μf(x)=0 in possesses a continuum of positive entire solutions, provided that (i) locally Hölder continuous functions K and f vanish rapidly, for instance, K(x),f(x)=O(|x|l) near ∞ for some l<−2 and (ii) μ≥0 is sufficiently small. Especially, in the radial case with K(x)=k(|x|) and f(x)=g(|x|) for some appropriate functions k,g on [0,∞), there exist two intervals Iμ,1, Iμ,2 such that for each α∈Iμ,1 the equation has a positive entire solution uα with uα(0)=α which converges to l∈Iμ,2 at ∞, and uα1<uα2 for any α1<α2 in Iμ,1. Moreover, the map α to l is one-to-one and onto from Iμ,1 to Iμ,2. If K≥0, each solution regarded as a steady state for the corresponding parabolic equation is stable in the uniform norm; moreover, in the radial case the solutions are also weakly asymptotically stable in the weighted uniform norm with weight function |x|n−2. 相似文献