A sufficient condition for the well posedness of a Goursat problem
A supersolution-subsolution method for nonlinear biharmonic equations in
A survey of partial differential equations with piecewise continuous arguments.
A survey of results on nonlinear Venttsel problems
We review the recent results for boundary value problems with boundary conditions given by second-order integral-differential operators. Particular attention has been paid to nonlinear problems (without integral terms in the boundary conditions) for elliptic and parabolic equations. For these problems we formulate some statements concerning a priori estimates and the existence theorems in Sobolev and Hölder spaces.
A symmetry result for a fourth order overdetermined boundary value problem.
A system of nonlinear degenerate parabolic equations.
A temperature control problem.
A theorem of Rolewicz's type for measurable evolution families in Banach spaces.
A Theorem on Elliptic Differential Inequalities with an Application to Gradient Bounds.
A topological invariant arising in the stability analysis of travelling waves.
A trace theorem for caloric functions.
A two-species cooperative Lotka-Volterra system of degenerate parabolic equations.
A unique continuation theorem for the wave equation in the exterior of a characteristic cone
A Uniqueness Theorem for Some Nonlinear Boundary Value Problems with a Large Parameter.
A variational analysis of a gauged nonlinear Schrödinger equation
This paper is motivated by a gauged Schrödinger equation in dimension 2 including the so-called Chern-Simons term. The study of radial stationary states leads to the nonlocal problem: , where . This problem is the Euler-Lagrange equation of a certain energy functional. In this paper the study of the global behavior of such functional is completed. We show that for , the functional may be bounded from below or not, depending on . Quite surprisingly, the threshold value for is explicit. From...
A variational approach in weighted Sobolev spaces to the operator - ... + .../... X1 in exterior domains of IR3.
A Variational Approach to Bifurcation in Lp on an Unbounded Symmetrical Domain.
A variational approach to bifurcation in reaction-diffusion systems with Signorini type boundary conditions
We consider a simple reaction-diffusion system exhibiting Turing's diffusion driven instability if supplemented with classical homogeneous mixed boundary conditions. We consider the case when the Neumann boundary condition is replaced by a unilateral condition of Signorini type on a part of the boundary and show the existence and location of bifurcation of stationary spatially non-homogeneous solutions. The nonsymmetric problem is reformulated as a single variational inequality with a potential...
A variational approach to bifurcation into spectral gaps
A variational approach to bifurcation points of a reaction-diffusion system with obstacles and Neumann boundary conditions
Given a reaction-diffusion system which exhibits Turing's diffusion-driven instability, the influence of unilateral obstacles of opposite sign (source and sink) on bifurcation and critical points is studied. In particular, in some cases it is shown that spatially nonhomogeneous stationary solutions (spatial patterns) bifurcate from a basic spatially homogeneous steady state for an arbitrarily small ratio of diffusions of inhibitor and activator, while a sufficiently large ratio is necessary in the...