Radial positive solutions for a nonpositone problem in a ball.
Radial solutions for a nonlocal boundary value problem.
Radial solutions of equations and inequalities involving the -Laplacian.
Radial solutions to a superlinear Dirichlet problem using Bessel functions.
Ranges of -homogeneous operators and their perturbations
Rapid convergence of approximate solutions for first order nonlinear boundary value problems.
Rapid Emergence of Co-colonization with Community-acquired and Hospital-Acquired Methicillin-Resistant Staphylococcus aureus Strains in the Hospital Setting
Background: Community-acquired methicillin-resistant Staphylococcus aureus (CA-MRSA), a novel strain of MRSA, has recently emerged and rapidly spread in the community. Invasion into the hospital setting with replacement of the hospital-acquired MRSA (HA-MRSA) has also been documented. Co-colonization with both CA-MRSA and HA-MRSA would have important clinical implications given differences in antimicrobial susceptibility profiles and the potential...
Rayleigh principle for linear Hamiltonian systems without controllability∗
In this paper we consider linear Hamiltonian differential systems without the controllability (or normality) assumption. We prove the Rayleigh principle for these systems with Dirichlet boundary conditions, which provides a variational characterization of the finite eigenvalues of the associated self-adjoint eigenvalue problem. This result generalizes the traditional Rayleigh principle to possibly abnormal linear Hamiltonian systems. The main tools...
Rayleigh principle for linear Hamiltonian systems without controllability∗
In this paper we consider linear Hamiltonian differential systems without the controllability (or normality) assumption. We prove the Rayleigh principle for these systems with Dirichlet boundary conditions, which provides a variational characterization of the finite eigenvalues of the associated self-adjoint eigenvalue problem. This result generalizes the traditional Rayleigh principle to possibly abnormal linear Hamiltonian systems. The main tools...
Realization theory methods for the stability investigation of nonlinear infinite-dimensional input-output systems
Realization theory for linear input-output operators and frequency-domain methods for the solvability of Riccati operator equations are used for the stability and instability investigation of a class of nonlinear Volterra integral equations in a Hilbert space. The key idea is to consider, similar to the Volterra equation, a time-invariant control system generated by an abstract ODE in a weighted Sobolev space, which has the same stability properties as the Volterra equation.
Reconstruction of map projection, its inverse and re-projection
This paper focuses on the automatic recognition of map projection, its inverse and re-projection. Our analysis leads to the unconstrained optimization solved by the hybrid BFGS nonlinear least squares technique. The objective function is represented by the squared sum of the residuals. For the map re-projection the partial differential equations of the inverse transformation are derived. They can be applied to any map projection. Illustrative examples of the stereographic and globular Nicolosi projections...
Rectifiability of solutions of the one-dimensional -Laplacian.
Reduction from a semi-infinite interval to a finite interval of a nonlinear boundary value problem for a system of second-order equations with a small parameter.
Reduction of an operator equation in to an equivalent bifurcation equation through Schauder's fixed point theorem.
Reguläre Eigenwertprobleme mit Mehrpunkt-Integral-Randbedingungen.
Regularized trace of the Sturm-Liouville operator with irregular boundary conditions.
Relative boundedness and compactness theory for second-order differential operators.
Relativistic wave equations with fractional derivatives and pseudodifferential operators.
Remark on Duffing equation with Dirichlet boundary condition.
Remarks on a three-point boundary value problem in a differential equation of the third order