We consider a nonlinear Neumann problem driven by the pLaplacianand with a concave parametric reaction term and an asymptotically linear pertur-bation. We prove a multiplicity theorem producing five nontrivial solutions all withsign information when the parameter is small. For the semilinear case (p = 2) weproduce six solutions, but we are unable to determine the sign of the sixth solution.Our approach uses critical point theory, truncation and comparison techniques andMorse theory.

Nonlinear noncoercive Neumann problems with a reaction concave near the origin / Candito, Pasquale; D'Aguì, G; Papageorgiou, N.. - In: TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS. - ISSN 1230-3429. - 47:1(2016), pp. 289-317. [10.12775/TMNA.2016.007]

Nonlinear noncoercive Neumann problems with a reaction concave near the origin

CANDITO, Pasquale
;
2016-01-01

Abstract

We consider a nonlinear Neumann problem driven by the pLaplacianand with a concave parametric reaction term and an asymptotically linear pertur-bation. We prove a multiplicity theorem producing five nontrivial solutions all withsign information when the parameter is small. For the semilinear case (p = 2) weproduce six solutions, but we are unable to determine the sign of the sixth solution.Our approach uses critical point theory, truncation and comparison techniques andMorse theory.
2016
Nonlinear noncoercive Neumann problem; multiple solutions; variational methods
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12318/3462
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