Critical Exponent for Semilinear Wave Equations with Space-Dependent Potential

The Nehari Manifold for a Class of Indefinite Weight Semilinear Elliptic Equations

On blowup for semilinear wave equations with a focusing nonlinearity

In this paper we report on numerical studies of formation of singularities for the semilinear wave equations with a focusing power nonlinearity utt−∆u = u in three space dimensions. We show that for generic large initial data that lead to singularities, the spatial pattern of blowup can be described in terms of linearized perturbations about the fundamental selfsimilar (homogeneous in space) so...

Asymptotic Behavior of Stochastic Wave Equations with Critical Exponents on R

The existence of a random attractor in H1(R3)×L2(R3) is proved for the damped semilinear stochastic wave equation defined on the entire space R 3. The nonlinearity is allowed to have a cubic growth rate which is referred to as the critical exponent. The uniform pullback estimates on the tails of solutions for large space variables are established. The pullback asymptotic compactness of the rand...

$L^p$-existence of mild solutions of fractional differential equations in Banach space

We study the existence of mild solutions for semilinear fractional differential equations with nonlocal initial conditions in $L^p([0,1],E)$, where $E$ is a separable Banach space. The main ingredients used in the proof of our results are measure of noncompactness, Darbo and Schauder fixed point theorems. Finally, an application is proved to illustrate the results of this work. 

Almost Global Existence for Some Semilinear Wave Equations with Almost Critical Regularity

For any subcritical index of regularity s > 3/2, we prove the almost global well posedness for the 2-dimensional semilinear wave equation with the cubic nonlinearity in the derivatives, when the initial data are small in the Sobolev space Hs × Hs−1 with certain angular regularity. The main new ingredient in the proof is an endpoint version of the generalized Strichartz estimates in the space Lt...