Stationary solutions of semilinear Schrödinger equations with trapping potentials in supercritical dimensions

Boundedness of Solutions for Duffing’s Equations with Semilinear Potentials

Existence of Global Solutions to Supercritical Semilinear Wave Equations

In this work we study the existence of global solution to the semilinear wave equation (∂

Exact solutions of semilinear radial wave equations in n dimensions

Exact solutions are derived for an n-dimensional radial wave equation with a general power nonlinearity. The method is based on the introduction of groupinvariant jet space variables associated with the point symmetry group admitted for the wave equation and is applicable more generally to any nonlinear PDEs. It is shown to yield not only group-invariant solutions as derived by standard symmetr...

Partial Regularity for Weak Solutions of Semilinear Elliptic Equations with Supercritical Exponents

Let Ω be an open subset in R (n ≥ 3). In this paper, we study the partial regularity for stationary positive weak solutions of the equation (1.1) ∆u + h1(x)u + h2(x)u = 0 in Ω. We prove that if α > n+2 n−2 , and u ∈ H(Ω) ∩ L(Ω) is a stationary positive weak solution of (1.1), then the Hausdorff dimension of the singular set of u is less than n−2α+1 α−1 , which generalizes the main results in Pa...

Stationary solutions, blow up and convergence to stationary solutions for semilinear parabolic equations with nonlinear boundary conditions

Unspecified Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: http://doi.org/10.5167/uzh-22758 Originally published at: Chipot, M; Fila, M; Quittner, P (1991). Stationary solutions, blow up and convergence to stationary solutions for semilinear parabolic equations with nonlinear boundary conditions. Acta Mathematica Universitatis Comenianae. New Series, 60(1):35-1...