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Three solutions for parametric problems with nonhomogeneous (a,2)-type differential operators and reaction terms sublinear at zero

Pasquale CanditoRoberto LivreaLeszek Gasiński

subject

PolynomialSublinear functionApplied Mathematics010102 general mathematicsMathematical analysisDifferential operator01 natural sciencesDirichlet distribution010101 applied mathematicssymbols.namesakeNonlinear systemSettore MAT/05 - Analisi Matematica(a2)-operator Constant sign solutions Nodal solutions Multiplicity of solutions Nonhomogeneous operatorsymbols0101 mathematicsLaplace operatorAnalysisSign (mathematics)MathematicsParametric statistics

description

Abstract We consider parametric Dirichlet problems driven by the sum of a Laplacian and a nonhomogeneous differential operator ( ( a , 2 ) -type equation) and with a reaction term which exhibits arbitrary polynomial growth and a nonlinear dependence on the parameter. We prove the existence of three distinct nontrivial smooth solutions for small values of the parameter, providing sign information for them: one is positive, one is negative and the third one is nodal.

yearjournalcountryeditionlanguage
2019-12-01Journal of Mathematical Analysis and Applications
https://doi.org/10.1016/j.jmaa.2019.123398