简介：<正>Inthispaper,weusetheordinarydifferentialequationtheoryofBanachspacesandminimaxtheory,andinparticular,therelativemountainpasslemmatostudysemilinearellipticboundaryvalueproblemswithjumpingnonlinearitiesatzeroorinfinity,andgetnewmultiplesolutionsandsign-changingsolutionstheorems,atlastwegetuptosixnontrivialsolutions.

简介：Inthispaper,theauthordiscussesthemultiplepositivesolutionsforaninfiniteboundaryvalueproblemoffirstorderimpulsivesuperlinearintegro-differentialequationsonthehalflinebymeansofthefixedpointtheoremofconeexpansionandcompressionwithnormtype.

简介：SlowmotionforscalarAllen-Cahntypeequationisawell-knownphenomenon,precisemotionlawforthedynamicsoffrontshavingbeenestablishedfirstusingthesocalledgeometricapproachinspiredfromcentralmanifoldtheory(seetheresultsofCarrandPegoin1989).Inthispaper,theauthorspresentanalternateapproachtorecoverthemotionlaw,andextendittothecaseofmultiplewells.Thismethodisbasedonthelocalizedenergyidentity,andistherefore,atleastconceptually,simplertoimplement.Italsoallowstohandlecollisionsandroughinitialdata.

简介：这篇论文与p拉普拉斯算符处理非线性的单个四点的边界价值问题的一个班的多重积极解决方案的存在：在哪儿φ(x)=|x|p−2x，p>1，(t)可能在t=是单个的0或t=1。由使用Leggett威廉，修理的固定的点定理和Schauder削尖定理，为存在的足够的条件多重(至少三)上述四点的边界值问题的积极答案被提供。说明获得的结果的重要性的一个例子也被给。

简介：

简介：MakinguseoftheZ2×Z2symmetry,wecouldstudythestructurenearmultipleS-treakingturningpoints.Inparticular,weshowthatthereexisttwokindsofsingularpointpaththroughdoubleSbreakingturningpointsandtripleSbieakingturningpoints,onetsquadraticturningporntpathandoneisquadraticpitchforkbifurcationpointpath.SomesimpleregularextendedsystemstocornputedoubleandtripleS-breakingturningpointsareproposed.Numericalexamplesarealsogreen