Existence of extremal periodic solutions for quasilinear parabolic equations.
Existence of global attractors in for -Laplacian parabolic equation in .
Existence of global solution for a nonlocal parabolic problem.
Existence of global solution of a nonlinear wave equation with short-range potential
Existence of global solutions for a predator-prey model with cross-diffusion.
Existence of global solutions for systems of reaction-diffusion equations on unbounded domains.
Existence of global solutions to a quasilinear wave equation with general nonlinear damping.
Existence of global solutions to reaction-diffusion systems via a Lyapunov functional.
Existence of Global Solutions to Supercritical Semilinear Wave Equations
∗The author was partially supported by Alexander von Humboldt Foundation and the Contract MM-516 with the Bulgarian Ministry of Education, Science and Thechnology.In this work we study the existence of global solution to the semilinear wave equation (1.1) (∂2t − ∆)u = F(u), where F(u) = O(|u|^λ) near |u| = 0 and λ > 1. Here and below ∆ denotes the Laplace operator on R^n. The existence of solutions with small initial data, for the case of space dimensions n = 3 was studied by F. John in [13],...
Existence of global solutions to the Cauchy problem for the seminlinear dissipative wave equations.
Existence of infinitely many solutions for elliptic boundary-value problems with nonsymmetrical critical nonlinearity.
Existence of least energy solutions to coupled elliptic systems with critical nonlinearities.
Existence of many positive nonradial solutions for a superlinear Dirichlet problem on thin annuli.
Existence of multiple solutions for a nonlinearly perturbed elliptic parabolic system in .
Existence of multiple solutions for a -Laplace equation.
Existence of nonnegative solutions to positone-type problems in with indefinite weights.
Existence of nontrivial solution for a nonlocal elliptic equation with nonlinear boundary condition.
Existence of periodic solutions for semilinear parabolic equations
In this paper, we are concerned with the semilinear parabolic equation ∂u/∂t - Δu = g(t,x,u) if u = 0 if , where is a bounded domain with smooth boundary ∂Ω and is T-periodic with respect to the first variable. The existence and the multiplicity of T-periodic solutions for this problem are shown when g(t,x,ξ)/ξ lies between two higher eigenvalues of - Δ in Ω with the Dirichlet boundary condition as ξ → ±∞.
Existence of periodic traveling wave solution to the forced generalized nearly concentric Korteweg-de Vries equation.
Existence of periodic traveling wave solutions to the generalized forced Boussinesq equation.