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ARBITRARILY sMALL NODAL sOLUTIONs FOR PARAMETRIC ROBIN(p,q)-EQUATIONs PLUs AN INDEFINITE POTENTIAL

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Acta Mathematica scientia 2022年第2期42卷 561-574页

作者： salvatore LEONARDI nikolaos s.papageorgiou Dipartimento di Matematica e Informatica Viale A.Doria695125 CataniaItaly Technical University Department of MathematicsZorografou CampusAthens 15780Greece

We consider a nonlinear Robin problem driven by the(p,q)-Laplacian plus an indefinite potential term and with a parametric reaction *** minimal conditions on the reaction function,which concern only its behavior near zero,we show that,for all λ>0 small,the problem has a nodal solution y_(λ)∈C^(1)(Ω)and we have y_(λ)→0 in C^(1)(Ω)asλ→0^(+).

关键词： (p,q)-Laplacian indefinite potential nonlinear regularity extremal constant sign solutions nodal solutions

ANIsOTROPIC(p,q)-EQUATIONs WITH COMPETITION PHENOMENA

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Acta Mathematica scientia 2022年第1期42卷 299-322页

作者： Zhenhai LIU nikolaos s.papageorgiou Guangxi Colleges and Universities Key Laboratory of Complex system Optimization and Big Data Processing Yulin Normal UniversityYulin 537000China Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis Guangxi University for NationalitiesNanning 530006China Department of Mathematics National Technical UniversityZografou Campus15780 Athens.Greece

We consider a nonlinear Robin problem driven by the anisotropic(p,q)-Laplacian and with a reaction exhibiting the competing effects of a parametric sublinear(concave) term and of a superlinear(convex) *** prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter *** also prove the existence of a minimal positive solution and determine the monotonicity and continuity properties of the minimal solution map.

关键词： concave-convex nonlinearities anisotropic operators regularity theory maximum principle minimal positive solution

sINGULAR DOUBLE PHAsE EQUATIONs

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Acta Mathematica scientia 2023年第3期43卷 1031-1044页

作者：刘振海 nikolaos s.papageorgiou Guangxi Colleges and Universities Key Laboratory of Complex system Optimization and Big Data Processing Yulin Normal UniversityYulin537000China Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis Guangxi Minzu UniversityNanning530006China Department of Mathematics National Technical UniversityZografou Campus15780AthensGreece

We study a double phase Dirichlet problem with a reaction that has a parametric singular term. Using the Nehari manifold method, we show that for all small values of the parameter, the problem has at least two positiv... 详细信息

关键词： double phase singular term unbalanced growth Musielak-Orlice spaces Nehari manifold positive solutions

POsITIVE sOLUTIONs FOR PARAMETRIC EQUIDIFFUsIVE p-LAPLACIAN EQUATIONs

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Acta Mathematica scientia 2014年第3期34卷 610-618页

作者： Leszek GAsINsKI nikolaos s.papageorgiou Jagiellonian University Faculty of Mathematics and Computer Scienceul. Lojasiewicza 630 348 KrakówPoland National Technical University Department of MathematicsZografou CampusAthens 15780Greece

We consider a parametric Dirichlet problem driven by the p-Laplacian with a Caratheodory reaction of equidiffusive type. Our hypotheses incorporate as a special case the equidiffusive p-logistic equation. We show that if λ1 〉 0 is the principal eigenvalue of the Dirichlet negative p-Laplacian and ）λ 〉 λ1 （/k being the parameter）, the problem has a unique positive solution, while for ）λ ∈ （0, λ1], the problem has no positive solution.

关键词： p-Laplacian p-logistic equation first eigenvalue equidiffusive reaction maxi-mum principle nonlinear regularity

LANDEsMAN-LAZER TYPE (p,q)-EQUATIONs WITH NEUMANN CONDITION

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Acta Mathematica scientia 2020年第4期40卷 991-1000页

作者： nikolaos s.papageorgiou Calogero VETRO Department of Mathematics National Technical UniversityZografou campusAthens 15780Greece Department of Mathematics and Computer science University of PalermoVia Archirafi 3490123PalermoItaly

We consider a Neumann problem driven by the(p,g)-Laplacian under the Landesman-Lazer type *** the classical saddle point theorem and other classical results of the calculus of variations,we show that the problem has a... 详细信息

关键词： Neumann problem (p,q)-Laplacian critical point saddle point theorem Landesman-Lazer type condition

Resonant-superlinear Nonhomogeneous Dirichlet Problems

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Acta Mathematica sinica,English series 2023年第11期39卷 2091-2116页

作者： Zhen Hai LIU nikolaos s.papageorgiou Center for Applied Mathematics of Guangxi Yulin Normal UniversityYulin 537000P.R.China Guangxi Key Laboratory of Universities Optimization Control and Engineering Calculation College of Mathematics and PhysicsGuangxi Minzu UniversityNanning 530006P.R.China Department of Mathematics National Technical UniversityZografou Campus15780 AthensGreece

We consider a Dirichlet nonlinear equation driven by the(p,2)-Laplacian and with a reaction having the competing effects of a parametric asymmetric superlinear term and a resonant *** show that for all small values of... 详细信息

关键词： Asymmetric reaction resonance superlinear term nonlinear regularity comparison principle critical groups solutions with sign information

Parametric Anisotropic(p,q)-Neumann Problems

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应用数学学报:英文版 2023年第4期39卷 926-942页

作者： Zhen-hai LIU nikolaos s.papageorgiou Center for Applied Mathematics of Guangxi Yulin Normal UniversityYulin 537000China Guangxi Key Laboratory of Universities Optimization Control and Engineering Calculation Guangxi Minzu UniversityNanning 530006China Department of Mathematics National Technical UniversityZografou Campus15780 AthensGreece

We consider a Neumann problem driven by a(p(z), q(z))-Laplacian(anisotropic problem) plus a parametric potential term with λ > 0 being the parameter. The reaction is superlinear but need not satisfy the Ambrosetti-Rabinowitz condition. We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter λ moves on R_(+)=(0,+∞).

关键词： variable exponent spaces superlinear reaction bifurcation-type theorem anisotropic regularity strong comparison positive solutions

sEMILINEAR HEMIVARIATIONAL INEQUALITIEs WITH sTRONG REsONANCE AT INFINITY

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Acta Mathematica scientia 2006年第1期26卷 59-73页

作者： Michael Filippakis Leszek Gasi■ski nikolaos s.papageorgiou Department of Mathematics National Technical University Zografou CampusAthens 15780Greece Institute of Computer science Jagiellonian University ul.Nawojki 1130072 CracowPoland

A semilinear elliptic equation with strong resonance at infinity and with a nonsmooth potential is studied. Using nonsmooth critical point theory and developing some abstract minimax principles which complement and ex... 详细信息

关键词： strong resonance hemivariational inequality Laplacian principal eigenvalue locally Lipschitz function Clarke subdifferential nonsmooth criticalpoint theory

MULTIPLE sOLUTIONs FOR NONAUTONOMOUs sECOND ORDER PERIODIC sYsTEMs

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Acta Mathematica scientia 2010年第1期30卷 350-358页

作者： Zdzislaw Denkowski Leszek Gasiński nikolaos s.papageorgiou Institute of Computer science Jagiellonian University Department of Mathematics National Technical UniversityZografou CampusAthens 15780Greece

We study nonautonomonus second order periodic systems with a nonslnooth potential. Using the nonsmooth critical theory, we establish the existence of at least two nontrivial solutions. Our framework incorporates large... 详细信息

关键词： locally Lipschitz potential generalized subdifferentiM coercive functional critical point local linking theorem nonsmooth Palais-smale condition multiple nontrivial solutions