A two parameters Ambrosetti-Prodi problem.
A Two-Particle Quantum System with Zero-Range Interaction
We study a two-particle quantum system given by a test particle interacting in three dimensions with a harmonic oscillator through a zero-range potential. We give a rigorous meaning to the Schrödinger operator associated with the system by applying the theory of quadratic forms and defining suitable families of self-adjoint operators. Finally we fully characterize the spectral properties of such operators.
A two-step Monge-Ampère procedure for solving a fourth order PDE for affine hypersurfaces with constant curvature.
A unified approach to a posteriori error estimation using element residual methods.
A uniform boundary Harnack inequality on non-tangentially accessible domains.
A uniformly accurate finite volume discretization for a convection-diffusion problem.
A unique continuation property for linear elliptic systems and nonresonance problems.
A uniqueness result for an inverse problem
We establish a uniqueness result for an overdetermined boundary value problem. We also raise a new question.
A uniqueness theorem for higher order elliptic partial differential equations.
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...
A variational characterization of the Fucík spectrum and applications.
A variational principle for complex boundary value problems.
A variational solution of the A. D. Aleksandrov problem of existence of a convex polytope with prescribed Gauss curvature
In his book on convex polytopes [2] A. D. Aleksandrov raised a general question of finding variational formulations and solutions to geometric problems of existence of convex polytopes in , n ≥ 2, with prescribed geometric data. Examples of such problems for closed convex polytopes for which variational solutions are known are the celebrated Minkowski problem [2] and the Gauss curvature problem [20]. In this paper we give a simple variational proof of existence for the A. D. Aleksandrov problem...
A variational treatment for general elliptic equations of the flame propagation type : regularity of the free boundary