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
Candito, P., Gasiński, L., Livrea, R. (2019). Three solutions for parametric problems with nonhomogeneous (a,2)-type differential operators and reaction terms sublinear at zero. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 480(1), 1-24 [10.1016/j.jmaa.2019.123398].
Three solutions for parametric problems with nonhomogeneous (a,2)-type differential operators and reaction terms sublinear at zero
Livrea, Roberto
2019-01-01
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
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