Showing papers in "Journal of Differential Equations in 1993"

TL;DR: In this article, interior and boundary Holder continuity for bounded weak soluttions of a class of quasilinear parabolic equations whose prototype is u t = div(|u| m − 1 |Du| p − 2 Du).

TL;DR: For autonomous differential equations in R n criteria are developed which preclude the existence of invariant closed curves such as periodic or homoclinic trajectories as discussed by the authors, based on the study of functionals on 2-surfaces.

TL;DR: In this paper, a smooth reversible vector field in R^4, such that the origin is a fixed point, is considered, where the differential at the origin has two double pure imaginary eigenvalues ± q for the critical value 0 of the parameter µ.

TL;DR: In this paper, a weak theory for the generalized mean curvature equation using the newly developed theory of viscosity solutions was developed, which is closely related to that of Osher and Sethian, Chen, Giga and Goto, and Evans and Spruck, who view the boundary of the crystal as the level set of a solution to a nonlinear parabolic equation.

TL;DR: In this paper, sufficient conditions are established for the global stability of the saturated equilibrium of an infinite delay, non-autonomous Lotka-Volterra type system, which relaxes the traditional requirement that the undelayed intraspecific competition dominates both the delayed intra-specific competition as well as the interspecific interactions.

TL;DR: In this paper, the existence and nonexistence of traveling wavefronts with speed c of the discrete Fisher′s equation u n = d(U n−1 − 2u n + u n+1 ) + ƒ(u n ), n ∈ Z, where d denotes a Lipschitz continuous function.

TL;DR: In this paper, the authors studied the nonlinear elliptic equation with the boundary condition (∗∗) u=0 on ∂Ω, where Ω is a bounded open subset of RN, and A(u) is a nonlinear operator of Leray-Lions type from W1,p0(Ω) into its dual, Φ∈(C0(R))N, g(x,t)t≥0, and f∈W−1, p′(ϵ)

TL;DR: In this article, the existence and regularity of solutions in RN to nonlinear elliptic equations of the form −div A(x, Du) + g (x, u) = ƒ was shown.

TL;DR: In this article, the authors show that the points in space-time at which smoothness is lost may even comprise an arbitrary discrete subset of the upper half-plane of the Korteweg-de-Vries equation.

TL;DR: In this paper, the authors established a local well-posedness result for a class of higher order nonlinear dispersive equations, including the next equation in the KdV hierarchy and some models appearing in water wave problems.

TL;DR: In this paper, a multiplicity of harmonic and subharmonic solutions to the periodically forced nonlinear Duffing's equation x + g(x) = p(t) in the semi-linear case was obtained.

TL;DR: In this article, an optimal control problem governed by a general class of quasilinear elliptic equations is studied, and the authors prove existence of solution and derive optimality conditions.

TL;DR: In this paper, the authors studied the appearance of limit cycles from the equator in polynomial vector fields with no singular points at infinity and showed that this bifurcation is a generalized Hopf bifurbcation from the point at infinity.

TL;DR: In this paper, the authors investigated the strong asymptotic stability of linear dynamical systems in Banach spaces, and showed that if the generator of a C0-semigroup is a C 0-isometric group, then there exists at least one pure imaginary λ = iβ ∈ σ(A ), the spectrum of A, and if A is only a 0isometric semigroup, but not a group, it is uniformly bounded and Re λ ≤ 0.

TL;DR: In this paper, the existence principles for systems of differential-difference equations of delay type are established and applications are given to first order delay equations, where the topological arguments are based on a nonlinear alternative.

TL;DR: In this article, the authors considered nonlinear parabolic equations of the form Δ u + ǫ( u ) and which are capable of exhibiting blow-up and showed that it is possible to choose initial conditions so that the solution is unbouded but exists, at least in a weak sense, for all time.

TL;DR: In this article, the existence of solutions for the Riemann problem of a mixed type system is established by a vanishing similarity viscosity approach, which is also admissible by the travelling wave criterion derived from the most common form of viscosities.