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In this article we present some results on the existence of positive and ground state solutions for the nonlinear Klein-Gordon-Maxwell equations. We introduce a general nonlinearity with subcritical a...
We consider a two-component system of semilinear wave equations in three space dimensions with quadratic nonlinear terms not satisfying the null condition. We prove small data global existence of the ...
Abstract: In this paper, we establish the existence and the regularity of a unique weak solution to turbulent flows in a bounded domain ${\Omega}\subset \mathbb R^3$ governed by the so-called Leray-{\...
We study a semilinear equation with derivatives satisfying a null condition on slowly rotating Kerr spacetimes. We prove that given sufficiently small initial data, the solution exists globally in tim...
Point-to-point re ection holding for harmonic functions subject to the Dirichlet or Neumann conditions on an analytic curve in the plane almost always fails for solutions to more general elliptic equ...
The mathematical physics literatures as well as quantum mechanics textbooks on spherically symmetric potentials are enormous. Despite of these there is no unique point of view about the boundary behav...
Consider the semiclassical limit, as the Planck constant ~ ! 0, of bound states of a quantum particle in a one-dimensional potential well. We justify the semiclassical asymptotics of eigenfunctions an...
In this paper, we investigate the interior regularity including the local boundedness and the interior H\"{o}lder continuity of weak solutions for parabolic equations of the $p(x,t)$-Laplacian type. W...
In this paper, we study the dynamical behavior for a 4-dimensional reversible system near its heteroclinic loop connecting a saddle-focus and a saddle. The existence of infinitely many reversible 1-ho...

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