Existence of periodic solutions for a class of nonlinear evolution equations.
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.
Existence of permanent and breaking waves for a shallow water equation : a geometric approach
The existence of global solutions and the phenomenon of blow-up of a solution in finite time for a recently derived shallow water equation are studied. We prove that the only way a classical solution could blow-up is as a breaking wave for which we determine the exact blow-up rate and, in some cases, the blow-up set. Using the correspondence between the shallow water equation and the geodesic flow on the manifold of diffeomorphisms of the line endowed with a weak Riemannian structure, we give sufficient...
Existence of positive and sign-changing solutions for -Laplace equations with potentials in .
Existence of positive bounded solutions for some nonlinear polyharmonic elliptic systems.
Existence of positive bounded solutions of semilinear elliptic problems.
Existence of positive entire solutions of semilinear elliptic equations on .
Existence of positive radial solutions for a weakly coupled systems via blow up.
Existence of positive radial solutions for the elliptic equations on an exterior domain
We discuss the existence of positive radial solutions of the semilinear elliptic equation ⎧-Δu = K(|x|)f(u), x ∈ Ω ⎨αu + β ∂u/∂n = 0, x ∈ ∂Ω, ⎩, where , N ≥ 3, K: [r₀,∞) → ℝ⁺ is continuous and , f ∈ C(ℝ⁺,ℝ⁺), f(0) = 0. Under the conditions related to the asymptotic behaviour of f(u)/u at 0 and infinity, the existence of positive radial solutions is obtained. Our conditions are more precise and weaker than the superlinear or sublinear growth conditions. Our discussion is based on the fixed point...
Existence of positive solutions for boundary value problems of nonlinear functional difference equation with -Laplacian operator.
Existence of positive solutions for Dirichlet problems of some singular elliptic equations.
Existence of positive solutions for higher order singular sublinear elliptic equations.
Existence of positive solutions for nonlinear boundary value problems in bounded domains of .
Existence of positive solutions for nonlinear boundary-value problems in unbounded domains of .
Existence of positive solutions for -Laplacian problems.
Existence of positive solutions for quasilinear elliptic systems involving the -Laplacian.
Existence of positive solutions for some Dirichlet problems with an asymptotically homogeneous operator.
Existence of positive solutions for some nonlinear elliptic systems on the half space.