A new approach to inverse spectral theory. II: General real potentials and the connection to the spectral measure.
A new approach to solve systems of second order non-linear ordinary differential equations.
A new approach to the existence results for orientor fields with Nicoletti's boundary conditions
Applying a global bifurcation theorem for convex-valued completely continuous mappings we prove some existence theorems for convex-valued differential inclusions of the form x'∈ F(t,x), where x satisfies the Nicoletti boundary conditions.
A new approach to Young measure theory, relaxation and convergence in energy
A new characteristic property of Mittag-Leffler functions and fractional cosine functions
A new characteristic property of the Mittag-Leffler function with 1 < α < 2 is deduced. Motivated by this property, a new notion, named α-order cosine function, is developed. It is proved that an α-order cosine function is associated with a solution operator of an α-order abstract Cauchy problem. Consequently, an α-order abstract Cauchy problem is well-posed if and only if its coefficient operator generates a unique α-order cosine function.
A new characterization of -bounded semigroups with application to implicit evolution equations.
A new continuous dependence result for impulsive retarded functional differential equations
We consider a large class of impulsive retarded functional differential equations (IRFDEs) and prove a result concerning uniqueness of solutions of impulsive FDEs. Also, we present a new result on continuous dependence of solutions on parameters for this class of equations. More precisely, we consider a sequence of initial value problems for impulsive RFDEs in the above setting, with convergent right-hand sides, convergent impulse operators and uniformly convergent initial data. We assume that the...
A new description and some modifications of Filippov cone
A new Green function concept for fourth-order differential equations.
A new instability result to nonlinear vector differential equations of fifth order.
A new iterative algorithm for solving the fictitious fluxes method problems for elliptic equations
A new look at an old comparison theorem
We present an integral comparison theorem which guarantees the global existence of a solution of the generalized Riccati equation on the given interval when it is known that certain majorant Riccati equation has a global solution on .
A new method for obtaining eigenvalues of variational inequalities. Branches of eigenvalues of the equation with the penalty in a special case
A new method for obtaining eigenvalues of variational inequalities based on bifurcation theory
A new method for the explicit integration of Lotka-Volterra equations.
A new method of proof of Filippov’s theorem based on the viability theorem
Filippov’s theorem implies that, given an absolutely continuous function y: [t 0; T] → ℝd and a set-valued map F(t, x) measurable in t and l(t)-Lipschitz in x, for any initial condition x 0, there exists a solution x(·) to the differential inclusion x′(t) ∈ F(t, x(t)) starting from x 0 at the time t 0 and satisfying the estimation where the function γ(·) is the estimation of dist(y′(t), F(t, y(t))) ≤ γ(t). Setting P(t) = x ∈ ℝn: |x −y(t)| ≤ r(t), we may formulate the conclusion in Filippov’s theorem...
A new model to describe the response of a class of seemingly viscoplastic materials
A new model is proposed to mimic the response of a class of seemingly viscoplastic materials. Using the proposed model, the steady, fully developed flow of the fluid is studied in a cylindrical pipe. The semi-inverse approach is applied to obtain an analytical solution for the velocity profile. The model is used to fit the shear-stress data of several supposedly viscoplastic materials reported in the literature. A numerical procedure is developed to solve the governing ODE and the procedure is validated...
A new oscillation criterion for forced second-order quasilinear differential equations.
A new phase space localization technique with application to the sum of negative eigenvalues of Schrödinger operators
A new proof of multisummability of formal solutions of non linear meromorphic differential equations
We give a new proof of multisummability of formal power series solutions of a non linear meromorphic differential equation. We use the recent Malgrange-Ramis definition of multisummability. The first proof of the main result is due to B. Braaksma. Our method of proof is very different: Braaksma used Écalle definition of multisummability and Laplace transform. Starting from a preliminary normal form of the differential equationthe idea of our proof is to interpret a formal power series solution...