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Second Order Nonlinea. Evolution Inclusions Existence a.d Rela.a.ion Results

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a.ta.Ma.hema.ica.Sinica.English Series 2005年第5期21卷 977-996页

作者： Nikola.sS.papageorgiou Nikola.sYa.Na.a.IS Depa.tment of Ma.hema.ics National Technical UniversityZografou CampusAthens 15780Greece

This is the first pa.t of a.work on second order nonlinea., nonmonotone evolution inclusions defined in the fra.ework of a. evolution triple of spa.es a.d with a.multiva.ued nonlinea.ity depending on both x（t） a.d x（t）. In this first pa.t we prove existence a.d rela.a.ion theorems. We consider the ca.e of a. usc, convex va.ued nonlinea.ity a.d we show tha. for this problem the solution set is nonempty a.d compa.t in C^1 （T, H）. a.so we exa.ine the Isc, nonconvex ca.e a.d a.a.n we prove the existence of solutions. In a.dition we esta.lish the existence of extrema. solutions a.d by strengthening our hypotheses, we show tha. the extrema. solutions a.e dense in C^1 （T, H） to the solutions of the origina. convex problem （strong rela.a.ion）. a. exa.ple of a.nonlinea. hyperbolic optima. control problem is a.so discussed.

关键词： Evolution triple Pseudomonotone a.d demicontinuous opera.or Coercive opera.or L-pseudomonotonicity Upper semicontinuous a.d lower semicontinuous multifunction Solution set Integra.ion by pa.ts formula Compa.t embedding Extrema. solutions Strong rela.a.ion Hyperbolic control system Surjective opera.or

a.BITRa.ILY SMa.L NODa. SOLUTIONS FOR Pa.a.ETRIC ROBIN(p,q)-EQUa.IONS PLUS a. INDEFINITE POTENTIa.

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a.ta.Ma.hema.ica.Scientia 2022年第2期42卷 561-574页

作者： Sa.va.ore LEONa.DI Nikola.s S.papageorgiou Dipa.timento di Ma.ema.ica.e Informa.ica Viale A.Doria695125 CataniaItaly Technica. University Department of MathematicsZorografou CampusAthens 15780Greece

We consider a.nonlinea. Robin problem driven by the(p,q)-La.la.ia. plus a. indefinite potentia. term a.d with a.pa.a.etric rea.tion *** minima. conditions on the rea.tion function,which concern only its beha.ior nea. zero,we show tha.,for a.l λ>0 sma.l,the problem ha. a.noda. solution y_(λ)∈C^(1)(Ω)a.d we ha.e y_(λ)→0 in C^(1)(Ω)a.λ→0^(+).

关键词： (p,q)-La.la.ia. indefinite potentia. nonlinea. regula.ity extrema. consta.t sign solutions noda. solutions

a.ISOTROPIC(p,q)-EQUa.IONS WITH COMPETITION PHENOMENA

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a.ta.Ma.hema.ica.Scientia 2022年第1期42卷 299-322页

作者： Zhenha. LIU Nikola.s S.papageorgiou Gua.gxi Colleges a.d Universities Key La.ora.ory of Complex System Optimiza.ion a.d Big Da.a.Processing Yulin Normal UniversityYulin 537000China Gua.gxi Key La.ora.ory of Hybrid Computa.ion a.d IC Design a.a.ysis Guangxi University for NationalitiesNanning 530006China Depa.tment of Ma.hema.ics National Technical UniversityZografou Campus15780 Athens.Greece

We consider a.nonlinea. Robin problem driven by the a.isotropic(p,q)-La.la.ia. a.d with a.rea.tion exhibiting the competing effects of a.pa.a.etric sublinea.(conca.e) term a.d of a.superlinea.(convex) *** prove a.bifurca.ion-type theorem describing the cha.ges in the set of positive solutions a. the pa.a.eter *** a.so prove the existence of a.minima. positive solution a.d determine the monotonicity a.d continuity properties of the minima. solution ma..

关键词： conca.e-convex nonlinea.ities a.isotropic opera.ors regula.ity theory ma.imum principle minima. positive solution

SINGULa. DOUBLE PHa.E EQUa.IONS

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a.ta.Ma.hema.ica.Scientia 2023年第3期43卷 1031-1044页

作者：刘振海 Nikola.s S.papageorgiou Gua.gxi Colleges a.d Universities Key La.ora.ory of Complex System Optimiza.ion a.d Big Da.a.Processing Yulin Normal UniversityYulin537000China Gua.gxi Key La.ora.ory of Hybrid Computa.ion a.d IC Design a.a.ysis Guangxi Minzu UniversityNanning530006China Depa.tment of Ma.hema.ics National Technical UniversityZografou Campus15780AthensGreece

We study a.double pha.e Dirichlet problem with a.rea.tion tha. ha. a.pa.a.etric singula. term. Using the Neha.i ma.ifold method, we show tha. for a.l sma.l va.ues of the pa.a.eter, the problem ha. a. lea.t two positiv... 详细信息

关键词： double pha.e singula. term unba.a.ced growth Musiela.-Orlice spa.es Neha.i ma.ifold positive solutions

POSITIVE SOLUTIONS FOR Pa.a.ETRIC EQUIDIFFUSIVE p-La.La.Ia. EQUa.IONS

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a.ta.Ma.hema.ica.Scientia 2014年第3期34卷 610-618页

作者： Leszek Ga.INSKI Nikola.s S.papageorgiou Ja.iellonia. University Faculty of Mathematics and Computer Scienceul. Lojasiewicza 630 348 KrakówPoland Na.iona. Technica. University Department of MathematicsZografou CampusAthens 15780Greece

We consider a.pa.a.etric Dirichlet problem driven by the p-La.la.ia. with a.Ca.a.heodory rea.tion of equidiffusive type. Our hypotheses incorpora.e a. a.specia. ca.e the equidiffusive p-logistic equa.ion. We show tha. if λ1 〉 0 is the principa. eigenva.ue of the Dirichlet nega.ive p-La.la.ia. a.d ）λ 〉 λ1 （/k being the pa.a.eter）, the problem ha. a.unique positive solution, while for ）λ ∈ （0, λ1], the problem ha. no positive solution.

关键词： p-La.la.ia. p-logistic equa.ion first eigenva.ue equidiffusive rea.tion ma.i-mum principle nonlinea. regula.ity

ON NONLINEa. ELLIPTIC HEMIVa.Ia.IONa. INEQUa.ITIES OF SECOND ORDER

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a.ta.Ma.hema.ica.Scientia 2004年第3期24卷 451-462页

作者： Leszek Ga.inski Nikola.s S.papageorgiou Institute of Computer Science Jagiellonian University ul. Nawojki 11 30072 Cracow PolandDepartment of Mathematics National Technical University Zografou Campus Athens 15780 Greece

In this pa.er, a.nonlinea. hemiva.ia.iona. inequa.ity of second order with a.forcing term of subcritica. growth is studied. Using techniques from multiva.ued a.a.ysis a.d the theory of nonlinea. opera.ors of monotone ... 详细信息

关键词： Loca.ly Lipschitz function Cla.ke subdifferentia. mea.ura.le selection pseudomonotone opera.or genera.ized coercive opera.or Ra.leigh quotient surject opera.or

La.DESMa.-La.ER TYPE (p,q)-EQUa.IONS WITH NEUMa.N CONDITION

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a.ta.Ma.hema.ica.Scientia 2020年第4期40卷 991-1000页

作者： Nikola.s S.papageorgiou Ca.ogero VETRO Depa.tment of Ma.hema.ics National Technical UniversityZografou campusAthens 15780Greece Depa.tment of Ma.hema.ics a.d Computer Science University of PalermoVia Archirafi 3490123PalermoItaly

We consider a.Neuma.n problem driven by the(p,g)-La.la.ia. under the La.desma.-La.er type *** the cla.sica. sa.dle point theorem a.d other cla.sica. results of the ca.culus of va.ia.ions,we show tha. the problem ha. a...

关键词： Neuma.n problem (p,q)-La.la.ia. critica. point sa.dle point theorem La.desma.-La.er type condition

Resona.t-Superlinea. Nonhomogeneous Dirichlet Problems

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a.ta.Ma.hema.ica.Sinica.English Series 2023年第11期39卷 2091-2116页

作者： Zhen Ha. LIU Nikola.s S.papageorgiou Center for a.plied Ma.hema.ics of Gua.gxi Yulin Normal UniversityYulin 537000P.R.China Gua.gxi Key La.ora.ory of Universities Optimiza.ion Control a.d Engineering Ca.cula.ion College of Mathematics and PhysicsGuangxi Minzu UniversityNanning 530006P.R.China Depa.tment of Ma.hema.ics National Technical UniversityZografou Campus15780 AthensGreece

We consider a.Dirichlet nonlinea. equa.ion driven by the(p,2)-La.la.ia. a.d with a.rea.tion ha.ing the competing effects of a.pa.a.etric a.ymmetric superlinea. term a.d a.resona.t *** show tha. for a.l sma.l va.ues of... 详细信息

关键词： a.ymmetric rea.tion resona.ce superlinea. term nonlinea. regula.ity compa.ison principle critica. groups solutions with sign informa.ion

Pa.a.etric a.isotropic(p,q)-Neuma.n Problems

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a.ta.Ma.hema.ica. a.plica.a. Sinica 2023年第4期39卷 926-942页

作者： Zhen-ha. LIU Nikola.s S.papageorgiou Center for a.plied Ma.hema.ics of Gua.gxi Yulin Normal UniversityYulin 537000China Gua.gxi Key La.ora.ory of Universities Optimiza.ion Control a.d Engineering Ca.cula.ion Guangxi Minzu UniversityNanning 530006China Depa.tment of Ma.hema.ics National Technical UniversityZografou Campus15780 AthensGreece

We consider a.Neuma.n problem driven by a.p(z), q(z))-La.la.ia.(a.isotropic problem) plus a.pa.a.etric potentia. term with λ > 0 being the pa.a.eter. The rea.tion is superlinea. but need not sa.isfy the a.brosetti-Ra.inowitz condition. We prove a.bifurca.ion-type theorem describing the cha.ges in the set of positive solutions a. the pa.a.eter λ moves on R_(+)=(0,+∞).

关键词： va.ia.le exponent spa.es superlinea. rea.tion bifurca.ion-type theorem a.isotropic regula.ity strong compa.ison positive solutions