Search results for "Critical group"

showing 4 items of 24 documents

Multiple solutions for semilinear Robin problems with superlinear reaction and no symmetries

2021

We study a semilinear Robin problem driven by the Laplacian with a parametric superlinear reaction. Using variational tools from the critical point theory with truncation and comparison techniques, critical groups and flow invariance arguments, we show the existence of seven nontrivial smooth solutions, all with sign information and ordered.

critical groupSettore MAT/05 - Analisi Matematicacritical point theoryConstant sign and nodal solutionsuperlinear reactionflow invariance
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(p,2)-equations resonant at any variational eigenvalue

2018

We consider nonlinear elliptic Dirichlet problems driven by the sum of a p-Laplacian and a Laplacian (a (p,2) -equation). The reaction term at ±∞ is resonant with respect to any variational eigenvalue of the p-Laplacian. We prove two multiplicity theorems for such equations.

multiple solution01 natural sciencesResonance (particle physics)Dirichlet distributionsymbols.namesakeSettore MAT/05 - Analisi Matematicavariational eigenvalues0101 mathematicsEigenvalues and eigenvectorsMathematicsNumerical AnalysisApplied Mathematics010102 general mathematicsMathematical analysisp-LaplacianMathematics::Spectral TheoryTerm (time)010101 applied mathematicsComputational MathematicsNonlinear systemresonancecritical groupsymbolsp-Laplaciannonlinear regularity theoryLaplacianLaplace operatorAnalysis
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Solutions with sign information for nonlinear Robin problems with no growth restriction on reaction

2019

We consider a parametric nonlinear Robin problem driven by a nonhomogeneous differential operator. The reaction is a Carathéodory function which is only locally defined (that is, the hypotheses concern only its behaviour near zero). The conditions on the reaction are minimal. Using variational tools together with truncation, perturbation and comparison techniques and critical groups, we show that for all small values of the parameter λ > 0, the problem has at least three nontrivial smooth solutions, two of constant sign and the third nodal.

nonlinear maximum principleApplied Mathematics010102 general mathematicsFunction (mathematics)Differential operator01 natural sciences010101 applied mathematicsNonlinear systemGrowth restrictionSettore MAT/05 - Analisi Matematicaextremal constant sign solutionsApplied mathematicsnodal solutions0101 mathematicscritical groupsAnalysisNonlinear regularity theorySign (mathematics)Parametric statisticsMathematicsApplicable Analysis
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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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