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- W1761146543 abstract "In this paper we consider a nonlinear parametric Dirichlet problem driven by a nonhomogeneous differential operator (special cases are the $p$-Laplacian and the $(p,q)$-differential operator) and with a reaction which has the combined effects of concave (($p-1)$-sublinear) and convex ($(p-1)$-superlinear) terms. We do not employ the usual in such cases AR-condition. Using variational methods based on critical point theory, together with truncation and comparison techniques and Morse theory (critical groups), we show that for all small $lambda>0$ ($lambda$ is a parameter), the problem has at least five nontrivial smooth solutions (two positive, two negative and the fifth nodal). We also prove two auxiliary results of independent interest. The first is a strong comparison principle and the second relates Sobolev and Hölder local minimizers for $C^1$ functionals." @default.
- W1761146543 created "2016-06-24" @default.
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- W1761146543 date "2014-12-01" @default.
- W1761146543 modified "2023-09-27" @default.
- W1761146543 title "Multiple and nodal solutions for nonlinear equations with a nonhomogeneous differential operator and concave-convex terms" @default.
- W1761146543 doi "https://doi.org/10.2748/tmj/1432229198" @default.
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