2 citations · 3 across the 10 of their papers we have counts for
10 papers
Hybrid Nehari-Schauder type fixed point results and applications
Radu Precup, Andrei Stan
This paper develops a fixed point version of the well-known Nehari manifold method from critical point theory. The main result is formulated for systems of operator equations, rely…
A Nehari manifold method for nonvariational problems
Radu Precup, Andrei Stan
The aim of this paper is to extend the Nehari manifold method from the variational setting to the nonvariational framework of fixed point equations. This is achieved by constructin…
Two abstract methods of lower and upper solutions with applications
Andrei Stan
In this paper, we present two abstract methods for constructing a lower and an upper solution for a fixed point equation. The first method applies when the nonlinear operator is a…
Control of semilinear differential equations with moving singularities
Radu Precup, Andrei Stan, Wei-Shih Du
In this paper, we present a control problem related to a semilinear differential equation with a moving singularity, i.e., the singular point depends on a parameter. The particular…
Critical point localization and multiplicity results in Banach spaces via Nehari manifold technique
Radu Precup, Andrei Stan
In the paper, results on the existence of critical points in annular subsets of a cone are obtained with the additional goal of obtaining multiplicity results. Compared to other ap…
Localization of critical points in annular conical sets via the method of Nehari manifold
Andrei Stan
Using the Nehari manifold method, we establish sufficient conditions such that a smooth functional attains a ground state within an annular domain of a closed cone. The localizatio…
Fixed point results and the Ekeland variational principle in vector -metric spaces
Radu Precup, Andrei Stan
In this paper, we extend the concept of \( b \)-metric spaces to the vectorial case, where the distance is vector-valued, and the constant in the triangle inequality axiom is repla…
On equilibrium in control problems with applications to evolution systems
Radu Precup, Andrei Stan
In this paper we examine a mutual control problem for systems of two abstract evolution equations subject to a proportionality final condition. Related observability and semi-obser…
A mutual control problem for semilinear system via fixed point approach
Radu Precup, Andrei Stan
In this paper, we introduce and discuss the concept of a mutual control problem. Our analysis relies on a vector fixed-point approach based on the fixed-point theorems of Perov, Sc…
Role of partial functionals in the study of variational systems
Andrei Stan
Applying techniques originally developed for systems lacking a variational structure, we establish conditions for the existence of solutions in systems that possess this property b…