Search results for "constant sign and nodal solutions"

showing 4 items of 4 documents

Constant sign and nodal solutions for nonlinear robin equations with locally defined source term

2020

We consider a parametric Robin problem driven by a nonlinear, nonhomogeneous differential operator which includes as special cases the p-Laplacian and the (p,q)-Laplacian. The source term is parametric and only locally defined (that is, in a neighborhood of zero). Using suitable cut-off techniques together with variational tools and comparison principles, we show that for all big values of the parameter, the problem has at least three nontrivial smooth solutions, all with sign information (positive, negative and nodal).

010102 general mathematicsMathematical analysisMathematics::Spectral Theory01 natural sciencesLocally defined reactionTerm (time)Critical groups010101 applied mathematicsNonlinear systemConstant sign and nodal solutionsSettore MAT/05 - Analisi MatematicaModeling and SimulationQA1-9390101 mathematicsNonlinear maximum principleConstant (mathematics)NODALMathematicsAnalysisSign (mathematics)MathematicsNonlinear regularity
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On Noncoercive (p, q)-Equations

2021

We consider a nonlinear Dirichlet problem driven by a (p, q)-Laplace differential operator (1 < q < p). The reaction is (p - 1)-linear near +/-infinity and the problem is noncoercive. Using variational tools and truncation and comparison techniques together with critical groups, we produce five nontrivial smooth solutions all with sign information and ordered. In the particular case when q = 2, we produce a second nodal solution for a total of six nontrivial smooth solutions all with sign information.

Dirichlet problemTruncationGeneral MathematicsMathematical analysisGeneral Physics and AstronomyDifferential operator(pq)-LaplacianNonlinear systemextremal solutionsprincipal eigenvalueSettore MAT/05 - Analisi Matematicanonlinear regularityconstant sign and nodal solutionsSign (mathematics)Mathematics
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A multiplicity theorem for parametric superlinear (p,q)-equations

2020

We consider a parametric nonlinear Robin problem driven by the sum of a \(p\)-Laplacian and of a \(q\)-Laplacian (\((p,q)\)-equation). The reaction term is \((p-1)\)-superlinear but need not satisfy the Ambrosetti-Rabinowitz condition. Using variational tools, together with truncation and comparison techniques and critical groups, we show that for all small values of the parameter, the problem has at least five nontrivial smooth solutions, all with sign information.

Pure mathematicsnonlinear maximum principlelcsh:T57-57.97General MathematicsMathematics::Analysis of PDEssuperlinear reactionMultiplicity (mathematics)extremal solutionsSettore MAT/05 - Analisi Matematicalcsh:Applied mathematics. Quantitative methodsConstant sign and nodal solutionExtremal solutionnonlinear regularityconstant sign and nodal solutionscritical groupsCritical groupMathematicsParametric statisticsOpuscula Mathematica
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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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