Cezar Avramescu

Existence problems for homoclinic solutions

The problem x ˙ = f ( t , x ) , x ( − ∞ ) = x ( + ∞ ) , where x ( ± ∞ ) : = lim t → ± ∞ x ( t ) ∈ ℝ n , is considered. Some existence results for this problem are established using the fixed point method and topological degree theory.

Homoclinic solutions for linear and linearizable ordinary differential equations

Using functional arguments, some existence results for the infinite boundary value problem x˙=F(t,x),x(−∞)=x(

Some general solvability theorems

Abstract In this paper, we study the solvability of a general equation of the form ƒ (χ) = 0 , with ƒ : E → F , where E and F are locally convex spaces or E = F and E is a Banach space. Our solvability results are based on some classical fixed-point theorems and on some geometrical conditions.

Conditional stability for a class of second-order differential equations ✩

Using two classes of test functions introduced recently by the authors, a criterion for conditional stability of the trivial solution of a second-order semi-linear differential equation is established.