Search results for "udc:517.956.2"

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Nonlinear Nonhomogeneous Robin Problems with Almost Critical and Partially Concave Reaction

2020

We consider a nonlinear Robin problem driven by a nonhomogeneous differential operator, with reaction which exhibits the competition of two Caratheodory terms. One is parametric, $$(p-1)$$-sublinear with a partially concave nonlinearity near zero. The other is $$(p-1)$$-superlinear and has almost critical growth. Exploiting the special geometry of the problem, we prove a bifurcation-type result, describing the changes in the set of positive solutions as the parameter $$\lambda >0$$ varies.

Competition phenomenacompetition phenomenanonlinear maximum principleAlmost critical growthLambda01 natural sciencesSet (abstract data type)symbols.namesakeMathematics - Analysis of PDEsSettore MAT/05 - Analisi Matematica0103 physical sciencesFOS: Mathematics0101 mathematicsbifurcation-type resultMathematicsParametric statisticsNonlinear regularity35J20 35J60010102 general mathematicsMathematical analysisZero (complex analysis)udc:517.956.2Differential operatorBifurcation-type resultalmost critical growthNonlinear systemDifferential geometryFourier analysissymbolsnonlinear regularity010307 mathematical physicsGeometry and TopologyNonlinear maximum principleStrong comparison principlestrong comparison principleAnalysis of PDEs (math.AP)
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Constant sign and nodal solutions for parametric anisotropic $(p, 2)$-equations

2021

We consider an anisotropic ▫$(p, 2)$▫-equation, with a parametric and superlinear reaction term.Weshow that for all small values of the parameter the problem has at least five nontrivial smooth solutions, four with constant sign and the fifth nodal (sign-changing). The proofs use tools from critical point theory, truncation and comparison techniques, and critical groups. Spletna objava: 9. 9. 2021. Abstract. Bibliografija: str. 1076.

udc:517.9electrorheological fluidsElectrorheological fluidMaximum principleMathematics - Analysis of PDEsSettore MAT/05 - Analisi MatematicaFOS: Mathematicsconstant sign and nodal solutionsAnisotropyanisotropic operators regularity theory maximum principle constant sign and nodal solutions critical groups variable exponent electrorheological fluidsParametric statisticsMathematicsvariable exponentVariable exponentApplied MathematicsMathematical analysisudc:517.956.2regularity theoryAnisotropic operatorsanisotropic operatorsTerm (time)Primary: 35J20 35J60 35J92 Secondary: 47J15 58E05maximum principleConstant (mathematics)critical groupsAnalysisAnalysis of PDEs (math.AP)Sign (mathematics)
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