Existence and Multiplicity of Solutions for Nonlinear Second-Order Differential Equations with Instantaneous and Non-Instantaneous Impulses via Variational Methods

Abstract

This paper explores a class of nonlinear second-order differential equations characterized by both instantaneous and non-instantaneous impulsive effects. We employ variational methods and critical point theory to investigate the existence and multiplicity of weak solutions. Specifically, we reformulate the problem as the minimization of an energy functional within an appropriate function space. Critical points of this energy function correspond to weak solutions of the impulsive problem under consideration. By imposing distinct growth conditions on the nonlinearities and impulsive functions, we rigorously establish the existence of at least one solution and infinitely many solutions for the considered problem. We present some examples to illustrate our results.TRANSLATE with x EnglishArabicHebrewPolishBulgarianHindiPortugueseCatalanHmong DawRomanianChinese SimplifiedHungarianRussianChinese TraditionalIndonesianSlovakCzechItalianSlovenianDanishJapaneseSpanishDutchKlingonSwedishEnglishKoreanThaiEstonianLatvianTurkishFinnishLithuanianUkrainianFrenchMalayUrduGermanMalteseVietnameseGreekNorwegianWelshHaitian CreolePersian   TRANSLATE with COPY THE URL BELOW Back EMBED THE SNIPPET BELOW IN YOUR SITE Enable collaborative features and customize widget: Bing Webmaster PortalBack