Stability of the Rayleigh-Ritz Procedure for Nonlinear Two-Point Boundary Value Problems.
Stationary solutions of semilinear Schrödinger equations with trapping potentials in supercritical dimensions
Nonlinear Schrödinger equations are usually investigated with the use of the variational methods that are limited to energy-subcritical dimensions. Here we present the approach based on the shooting method that can give the proof of existence of the ground states in critical and supercritical cases. We formulate the assumptions on the system that are sufficient for this method to work. As examples, we consider Schrödinger-Newton and Gross-Pitaevskii equations with harmonic potentials.
Strong resonance problems for the one-dimensional -Laplacian.
Strong uniform approximation for some singularly perturbed differential equations arising in chemical reactor theory.
Studies on BVPs for IFDEs involved with the Riemann-Liouville type fractional derivatives
In this article, we present a new method for converting the boundary value problems for impulsive fractional differential systems involved with the Riemann-Liouville type derivatives to integral systems, some existence results for solutions of a class of boundary value problems for nonlinear impulsive fractional differential systems at resonance case and non-resonance case are established respectively. Our analysis relies on the well known Schauder’s fixed point theorem and coincidence degree theory....
Sturm-Liouville and focal higher order BVPs with singularities in phase variables.
Sufficient condition for existence of solutions for higher-order resonance boundary value problem with one-dimensional p-Laplacian.
Sufficient conditions for the solvability of some third order functional boundary value problems on the half-line
This paper is concerned with the existence of bounded or unbounded solutions to third-order boundary value problem on the half-line with functional boundary conditions. The arguments are based on the Green functions, a Nagumo condition, Schauder fixed point theorem and lower and upper solutions method. An application to a Falkner-Skan equation with functional boundary conditions is given to illustrate our results.
Sur les équations du type Ψ(x,h)=0 (II)
Sur un problème aux limites de la théorie du transfert de masse et de chaleur
Surjectivity and boundary value problems
Surjectivity of an operator
Symmetric equilibria for a beam with a nonlinear elastic foundation.
System of fractional differential equations with Erdélyi-Kober fractional integral conditions
In this paper we study existence and uniqueness of solutions for a system consisting from fractional differential equations of Riemann-Liouville type subject to nonlocal Erdélyi-Kober fractional integral conditions. The existence and uniqueness of solutions is established by Banach’s contraction principle, while the existence of solutions is derived by using Leray-Schauder’s alternative. Examples illustrating our results are also presented.
Systems of singular BVPs - existence of solutions and their properties
We discuss the existence and properties of solutions for systems of singular second-order ODEs in both sublinear and superlinear cases. Our approach is based on the variational method enriched by some topological ideas. We also investigate the continuous dependence of solutions on functional parameters.