Morse theory and local linking for a class of boundary value problems with impulsive effects

Abstract

In this paper we study a class of boundary value problems with impulsive effects. By using Morse theory in combination with local linking arguments, the existence results of at least one nontrivial solution are obtained when the nonlinearity f is not linear.

Applications of Morse Theory to Fourth-Order Impulsive Differential Equations ∗

“…Motivated by above facts, it is clear to see the methods to deal with these fourth-order boundary value problems are variational methods and some critical point theory. But as far as we know, Morse theory is an important method in nonlinear analysis which can also be a powerful tool to study the existence of solutions for differential equations (see [23][24][25] and references therein). However, Morse theory has not received so much attention as variational method and critical point theory, and also it should be pointed out that there is no published paper which has discussed the existence of solutions for fourth-order boundary value problems by using Morse theory.…”

The existence of solutions for perturbed fractional differential equations with impulses via Morse theory

“…On the other hand, in recent years, Morse theory has been used to discuss the existence of solutions of differential equations [25,26]. However, to the best of our knowledge, Morse theory is rarely applied to the impulsive fractional boundary-value problems.…”

Extreme Feature Regions Detection and Accurate Quality Assessment for Point-Cloud 3D Reconstruction

“…(1) We present a new tree-structure-based algorithm, inspired by the Morse theory [16], [17], to find the precise extreme feature regions in images. The extreme regions can help to calculate the affine transformation matrix by the saddle points to normalize the affine images in SfM and get precise features.…”