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Showing papers in "Journal of Differential Equations in 1999"


Journal ArticleDOI
TL;DR: In this article, the existence and non-existence results on non-constant positive solutions of (1.1) have been established for a variety of multidimensional existence, non-convexity, intra-specific and inter-specific competitions.

265 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that the dimension N = 3 is a critical dimension for solving (1.1) problems, and that dimension N is a special dimension if compared with N = 4.

254 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that the problem has interior spike solutions at a local maximum point of the distance function d(P, ∂Ω), P e Ω, where Ω is a bounded smooth domain in RN, ǫ > 0 is a small parameter, and ƒ is a superlinear, subcritical nonlinearity.

243 citations


Journal ArticleDOI
TL;DR: In this paper, a nontrivial solution u. has been proposed for the problem of finding a solution for 7p in the linear case, where u is defined as a non-negative integer in (1.1).

218 citations


Journal ArticleDOI
TL;DR: In this article, the rate and profile of blow-up of diffusion equations with nonlocal nonlinear reaction terms were investigated and sharp estimates on the size of boundary layer and on the asymptotic behavior of the solution in the boundary layer were derived.

215 citations


Journal ArticleDOI
TL;DR: The main aim of as discussed by the authors is to establish stochastic versions of the well-known LaSalle stability theorem from classical results on stochastically stable systems, which follow many classical results.

213 citations


Journal ArticleDOI
TL;DR: In this paper, a singular perturbation theory for initial value problems of nonlinear first-order hyperbolic systems with stiff source terms in several space variables is developed, and formal asymptotic approximations of the initial-layer solution to the nonlinear problem are given.

181 citations


Journal ArticleDOI
TL;DR: In this paper, the exact shape of the global bifurcation diagram is rigorously proved for a wide class of nonlinear functions ǫ(u)/ǫ.

180 citations


Journal ArticleDOI
TL;DR: In this article, a general class of degenerate elliptic-paraboic problems associated with the equation b(v)(t) = div a(v, Dv) + f was considered.

171 citations


Journal ArticleDOI
TL;DR: In this paper, a class of coupled hyperbolic systems of conservation laws which contain the one-dimensional zero-pressure gas dynamics was studied constructively and all of the existence, uniqueness, and stability of solutions to viscous perturbations were proved.

137 citations


Journal ArticleDOI
Wenxian Shen1
TL;DR: In this paper, the authors introduced the concept of almost periodic traveling wave solutions and established the stability and uniqueness of such solutions to time almost periodic bistable nonlinear equations with one dimensional continuous space variable.

Journal ArticleDOI
TL;DR: The notion of integrability of flows or vector fields on two-dimensional manifolds has been studied in this paper, where it is shown that every local flow ϕ on a 2D manifold has a continuous first integral on each component of the manifold, where ϕ is the set of all separatrices of ϕ.

Journal ArticleDOI
TL;DR: In this article, the authors prove existence, uniqueness and regularity of solutions for heat equations with nonlinear boundary conditions, with initial data in L-q(Omega), W-1, W-q-Omega, 1 < q < infinity or measures and with critically growing nonlinearities.

Journal ArticleDOI
TL;DR: In this paper, the authors prove comparison results between viscosity sub-and supersolutions of degenerate elliptic and parabolic equations associated with nonlinear Neumann boundary conditions.

Journal ArticleDOI
TL;DR: In this paper, the authors considered the nth eigenvalue as a function on the space of self-adjoint regular Sturm-Liouville problems with positive leading coefficient and weight functions.

Journal ArticleDOI
TL;DR: In this article, explicit estimates for the continuous dependence in L∞([0, T]; L1(Rd)) of solutions of the equation ∂lv=∇·(Φ(v))+Δ(ϕ(v)), with initial conditionv(0, ·)=h) with respect to the nonlinear continuously differential functionsΦ andϕ are established.

Journal ArticleDOI
Wenxian Shen1
TL;DR: In this article, a series of two papers is concerned with traveling wave solutions of time almost periodic nonlinear evolution equations and the existence of such solutions for bistable equations with continuous space variables.

Journal ArticleDOI
TL;DR: In this paper, the authors studied the range of the operatoru↦(|u′|p−2u′)′+λ1/(πpt/T) −1/p), and showed that if p≠2 and h≢0 the solution set is bounded.

Journal ArticleDOI
TL;DR: In this article, the authors studied isochronous centers of analytic Hamiltonian systems giving special attention to the polynomial case and showed the connection between isochronicity and involutions.

Journal ArticleDOI
Jiangong You1
TL;DR: In this article, a generalized Kolmogorov-Arnold-Moser theorem for lower dimensional tori in Hamiltonian systems is presented, based on Newton's iteration method and a generalized version of small divisor conditions.

Journal ArticleDOI
TL;DR: In this paper, the authors prove higher integrability for minimizers with nonstandard growth conditions of (p, q) type, where q satisfies a non standard growth condition.

Journal ArticleDOI
TL;DR: In this article, the radial symmetry and asymptotic behavior of positive solutions of Δu=ϕ(|x|) u λ, x∈ R n and |x| large where λ > 1 and ϕ ( r ) is positive and continuous for r large.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the contractivity of weak solutions to conservation laws with different flux functions is bounded by the total variation with respect to the space variable, of the difference between the flux functions.

Journal ArticleDOI
TL;DR: In this paper, the period function of a center of a Lienard system is studied and sufficient conditions for monotonicity and isochronicity of the center are given.

Journal ArticleDOI
TL;DR: In this article, the authors consider the asymptotic behavior of solutions to the p-system with linear damping on the half-line R+=(0, ∞),vt−ux=0,ut+p(v)x=−αu, with the Dirichlet boundary condition u|x=0=0 or the Neumann boundary conditionux|x =0 =0.

Journal ArticleDOI
TL;DR: An upper bound of B(n)⩽7n+5 for the number of zeros of Abelian integrals was derived in this article, where n is the maximal interval of existence of an algebraic curve.

Journal ArticleDOI
TL;DR: In this article, the authors study the initial value problem for the system of compressible adiabatic flow through porous media in the one space dimension with fixed boundary condition and establish the global existence and large time behavior for the classical solutions via the combination of characteristic analysis and energy estimate methods.

Journal ArticleDOI
TL;DR: In this article, it was shown that the boundary value problem has infinitely many solutions provided V is even and super-quadratic, and that V is super-squadratic.

Journal ArticleDOI
TL;DR: In this paper, a new criterion of global solvability for smooth axisymmetric solutions of the 3D Euler equations for a cylindrical type of domain, which can be whole R3, was proposed.

Journal ArticleDOI
TL;DR: In this article, the existence and symmetry property of multi-bump solutions of −Δv+λV(x)v=vp,v>0,inRN was studied and conditions were given to assure that the multibump solutions obtained have prescribed subgroups of O(N) as their exact symmetry.