Existence, uniqueness, and regularity of solutions to semilinear retarded differential equations.
Existence, uniqueness and stability results of impulsive stochastic semilinear neutral functional differential equations with infinite delays.
Existence-uniqueness and iterative methods for right focal point boundary value problems for differential equations with deviating arguments
Existenz und erste Einschließung positiver Lösungen bei superlinearen Randwertaufgaben zweiter Ordnung. -Existence and First Bounds of Positive Solutions of Superlinear Second-Order Boundary Value Problems.
Expansion for the superheating field in a semi-infinite film in the weak- limit
Dorsey, Di Bartolo and Dolgert (Di Bartolo et al., 1996; 1997) have constructed asymptotic matched solutions at order two for the half-space Ginzburg-Landau model, in the weak- limit. These authors deduced a formal expansion for the superheating field in powers of up to order four, extending the formula by De Gennes (De Gennes, 1966) and the two terms in Parr’s formula (Parr, 1976). In this paper, we construct asymptotic matched solutions at all orders leading to a complete expansion in powers...
Expansion for the superheating field in a semi-infinite film in the weak-κ limit
Dorsey, Di Bartolo and Dolgert (Di Bartolo et al., 1996; 1997) have constructed asymptotic matched solutions at order two for the half-space Ginzburg-Landau model, in the weak-κ limit. These authors deduced a formal expansion for the superheating field in powers of up to order four, extending the formula by De Gennes (De Gennes, 1966) and the two terms in Parr's formula (Parr, 1976). In this paper, we construct asymptotic matched solutions at all orders leading to a complete expansion...
Expansion of solutions of T'Hooft's equation. A study in the confluence of analytic boundary conditions.
Expansional in banach algebras
Expected utility maximization and conditional value-at-risk deviation-based Sharpe ratio in dynamic stochastic portfolio optimization
In this paper we investigate the expected terminal utility maximization approach for a dynamic stochastic portfolio optimization problem. We solve it numerically by solving an evolutionary Hamilton-Jacobi-Bellman equation which is transformed by means of the Riccati transformation. We examine the dependence of the results on the shape of a chosen utility function in regard to the associated risk aversion level. We define the Conditional value-at-risk deviation () based Sharpe ratio for measuring...
Explicit asymptotic stability criteria for neutral differential equations with two delays.
Explicit bounds on some nonlinear integral inequalities.
Explicit conditions for stability of nonlinear scalar delay impulsive difference equation.
Explicit construction, uniqueness, and bifurcation curves of solutions for a nonlinear Dirichlet problem in a ball.
Explicit rational solutions of Knizhnik-Zamolodchikov equation
We consider the Knizhnik-Zamolodchikov system of linear differential equations. The coefficients of this system are rational functions generated by elements of the symmetric group n. We assume that parameter ρ = ±1. In previous paper [5] we proved that the fundamental solution of the corresponding KZ-equation is rational. Now we construct this solution in the explicit form.
Explicit solution for Lamé and other PDE systems
We provide a general series form solution for second-order linear PDE system with constant coefficients and prove a convergence theorem. The equations of three dimensional elastic equilibrium are solved as an example. Another convergence theorem is proved for this particular system. We also consider a possibility to represent solutions in a finite form as partial sums of the series with terms depending on several complex variables.
Explicit solutions for boundary value problems related to the operator equations
Cauchy problem, boundary value problems with a boundary value condition and Sturm-Liouville problems related to the operator differential equation are studied for the general case, even when the algebraic equation is unsolvable. Explicit expressions for the solutions in terms of data problem are given and computable expressions of the solutions for the finite-dimensional case are made available.
Explicit solutions for non homogeneous Sturm-Liouville operators problems.
In this paper we study existence and sufficiency conditions for the solutions of Sturm-Liouville operator problems related to the operator differential equation X'' - QX = F(t). Explicit solutions of the problem in terms of a square root of the operator Q are given.
Explicit solutions for Sturm-Liouville operator problems (II).
It is proved that the resolution problem of a Sturm-Liouville operator problem for a second-order differential operator equation with constant coefficients is solved in terms of solutions of the corresponding algebraic operator equation. Existence and uniqueness conditions for the existence of nontrivial solutions of the problem and explicit expressions of them are given.
Explicit Solutions of Several Kummer's Nonlinear Differential Equations
Explicit Solutions of Two-Point Boundary Value Operator Problems.