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1、共振条件下二阶积分边值问题解存在性（英文）Thetheoryofboundaryvalueproblemswithintegralboundaryconditionsforordinarydifferentialequationsarisesindifferentareasofappliedmathematicsandphysics.Forexample,heatconduction,chemicalengineering,undergroundwaterflow,thermo-elasticity,andplasmaphysicscanbe
2、reducedtothenonlocalproblemswithintegralboundaryconditions・Moreover,boundaryvalueproblemswithRiemann-Stieltjesintegralconditionsconstituteaveryinterestingandimportantclassofproblems・Theyincludetwo,three,multi-pointandintegralboundary-valueproblemsasspecialcases,see[1,2,3,4]
3、・Theexistenceandmultiplicityofsolutionsforsuchproblemshavereceivedagreatdealofattentions.Wereferthereaderto[5,6,7,8]forsomerecentresultsatnonresonance・Tothebestofourknowledge,thereareonlyfewpublishedpapersthatdealwiththeexistenceofsolutionsforlocal,nonlocaland,particularly,
4、integralnonlocalboundaryvalueproblemsatresonance(see[9-18])・In[16],MagaveanexistenceresuItforsolutionsforthethree-pointboundaryvalueproblemInthispaper,weshallestablishatheoremofexistenceofsolutionfortheproblem(1)and(2)atresonancebyemployingthemethodsofloweranduppersolutions
5、.Clearly,wegeneralizethemainresuItsof[10,16].Theproofsofthemethodsofloweranduppersolutionarebasedontheconnectivitypropertiesofthesolutionsetsofparameterizedfamiliesofcompactvectorfields；theyareadirectconsequenceofMawhin[19,20].Acontradiction!ThisimpliesthattO二0ortO二1andther
6、eareonlythreecasestoconsider：Case1:Thereare00foralltw[0,£)U(r],1J;forCase2：ThereisEWalltW[0,E]andv(0,(t)1)such0forthatallv(t)W01J;forCase3：Thereisr]W(0,alltG[r],1]andv(t)1)suchthatv(t)W0forallt丘[0，H)・WeonlyproveCase1,theothersaresimilarBythesameargument,weseethaty(t)Wu(t)，f
7、ortG[0,1].Sincey(t)Wu(t)Wx(t)fortw[0,1],itfollowsthatf二f?,andsouisasolutionofproblems(1)and(2).Theproofiscomplete・Theorem2Supposef:[0,1]XRfRiscontinuous・Ifthereexiststrictuppersolutionxandstrictlowersolutionyofproblems(1)and(2)withy(t)Wx(t)fort£[0,1],thenproblems(1)and(2)ha
8、sasolutionu^D.Therefore,bytheconnectivityof》，theremustexistsomecOW(c2,cl)andw(cO)W
