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Showing papers in "Journal of Differential Equations in 1991"


Journal ArticleDOI
TL;DR: In this paper, it was shown that every weak solution to (1.1) of class?4' is locally Lipschitz-continuous in Q. Under some other assumptions, by assuming also that the quotient q/p is sufficiently close to one in dependence on n (precisely, if q /p c n/(n 2)), then we can show that if q 2 p c n 2 2 2

684 citations


Journal ArticleDOI
TL;DR: In this article, the authors considered the semilinear parabolic system (S) and showed that if 0 T ∗ = + ∞, then the Cauchy problem can be continued for all positive times.

327 citations


Journal ArticleDOI
TL;DR: In this paper, the authors considered the blow-up of the solution in H1 for the following nonlinear Schrodinger equation: i∂∂tu + Δu = −¦u¦p − 1u, x ϵ Rn, t ⩾ 0, (∗) u(0, x) = u0(X), xπ Rn. t = 0, where n 2 and 1 + 4/n ⩽ p < min {(n + 2)(n − 2), 5}.

274 citations


Journal ArticleDOI
TL;DR: In this article, the authors studied the limiting behavior of u = U' as E + 0 and showed that the solutions of (1.1) are in a certain sense compact as functions of space-time.

264 citations


Journal ArticleDOI
Xu-Jia Wang1
TL;DR: In this paper, the existence of a positive solution to the Neumann boundary condition for α(x) = 0 was proved under an additional assumption on the boundary ∂Ω.

228 citations



Journal ArticleDOI
TL;DR: In this article, a model for a gel-permeation chromatograph was derived by the method of homogenization and the resulting equations could be applied to real chromatographs with a surprising agreement between experimental data and results obtained by the theoretical model.

177 citations



Journal ArticleDOI
TL;DR: In this article, the authors studied the existence of travelling wave solutions and the property of finite propagation for the reaction-diffusion equation and showed that travelling waves exist globally only if m + n = 2 and only for velocities ¦c¦ ⩾ c ∗ = 2 √λm.

145 citations


Journal ArticleDOI
TL;DR: In this paper, a differential-geometric approach for proving the existence and uniqueness of implicit differential-algebraic equations is presented, which provides for a significant improvement of an earlier theory developed by the authors as well as for a completely intrinsic definition of the index of such problems.

144 citations


Journal ArticleDOI
TL;DR: In this paper, the number and position of the local families of limit cycles which emerge from the periodic trajectories surrounding an isochronous (or linearizable) center were determined for a one parameter family of plane quadratic vector fields X (.,e) depending analytically on a small real parameter e.

Journal ArticleDOI
TL;DR: In this paper, the authors give a geometric construction of heteroclinic and homocliic orbits for singularly perturbed differential equations and derive analytical conditions for transversality.

Journal ArticleDOI
TL;DR: In this article, the authors consider a linear system in Rmfn and show that if each leaf is used as a coordinate, the original system is completely decoupled and the linearization follows easily.

Journal ArticleDOI
TL;DR: In this article, the authors extended the theory to obtain some improvements in the results of Hirsch and Matano under Matano's weaker assumption that the semiflow is strongly order preserving, and they applied the convergence results developed in [ 131 to nonquasimonotone FDEs.

Journal ArticleDOI
TL;DR: In this paper, the authors give conditions which guarantee that products of solutions of partial differential equations Pu + au = 0 are complete in L 2 (Ω) where P is a linear partial differential operator with constant coefficients, and a is a function in L ∞ (ϵ).

Journal ArticleDOI
TL;DR: In this paper, the authors consider the planar motion of a uniform prismatic beam of length L and derive a model that reflects the effect of stretching on bending, which necessarily leads to nonlinear partial differential equations for the motion of the beam.

Journal ArticleDOI
TL;DR: Lasiecka and Triggiani as mentioned in this paper studied the regularity of solutions of general, mixed, second-order, time-dependent, hyperbolic problems of Neumann type using pseudo-differential calculus.

Journal ArticleDOI
TL;DR: In this article, the authors studied positive solutions of the semilinear elliptic equation without trivial solutions, where the nonlinearity is subcritical, which roughly speaking means that g(x, u) 1~1 -(N+2MN--2) goes to 0 as 1~ 1 -+ cc (at least if Na 3).

Journal ArticleDOI
TL;DR: In this article, the existence of homoclinic orbits for a first order Hamiltonian system z = JH z (t, z) is studied and a nontrivial solution z∞(t) and subharmonic solutions (zT(t))TϵN (i.e., 2πT-periodic solutions) of (HS) such that ZT → Z∞ (t) in Cloc1(R, R 2N) as T → ∞.

Journal ArticleDOI
TL;DR: In this paper, the authors studied the large time behavior of positive solutions of the heat equation under the nonlinear boundary condition ∂u ∂ν = f(u), where η is the outward normal and f is non-decreasing with f (u) > 0 for u > 0.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the generalized Benjamin-Ono equation exhibits smoothing properties similar to those of the generalized Korteweg-de Vries equation (GKdV), which is the special case μ = 1 of (∗), if V satisfies suitable estimates at zero and at infinity.

Journal ArticleDOI
R Datko1
TL;DR: In this paper, the qualitative behavior of a given stabilizing feedback for such a system vis a vis that of an appropriately damped realization using the same feedback is investigated. And the robustness of both the original system and a damped version when time delays occur in a given feedback stabilization scheme.


Journal ArticleDOI
Zhihong Xia1
TL;DR: In this paper, the exact number of central configurations for some open sets of n positive masses for any choice of n was found. But the number of configurations is not the same for all positive masses.

Journal ArticleDOI
TL;DR: In this article, sufficient conditions are derived for the global existence of a weak solution to a strictly hyperbolic nonlinear system of partial differential equations in one space dimension when the initial data is a small BV perturbation of a solvable Riemann problem.




Journal ArticleDOI
TL;DR: In this paper, the perturbation theory of invariant surface has been used to find inertial manifolds in the infinite dimensional setting by replacing the first order equation for Φ by the regularized elliptic equation −eΔΦ + DΦ(p) G1,(p, Φ(P)) + AΦ (p) = G2(p.