DCDS
Critical points for a class of nondifferentiable functions and applications
P. Candito S. A. Marano D. Motreanu
Some critical point theorems involving functionals that are the sum of a locally Lipschitz continuous term and of a convex, proper, besides lower semicontinuous, function are established. A recent existence result of Adly, Buttazzo, and Théra [1, Theorem 2.3] is improved. Applications to elliptic variational-hemivariational inequalities are then examined.
keywords: Critical points of non-smooth functions variational-hemivariational inequalities.
CPAA
Nonautonomous resonant periodic systems with indefinite linear part and a nonsmooth potential
D. Motreanu V. V. Motreanu Nikolaos S. Papageorgiou
A nonautonomous second order system with a nonsmooth potential is studied. It is assumed that the system is asymptotically linear at infinity and resonant (both at infinity and at the origin), with respect to the zero eigenvalue. Also, it is assumed that the linearization of the system is indefinite. Using a nonsmooth variant of the reduction method and the local linking theorem, we show that the system has at least two nontrivial solutions.
keywords: reduction method Resonant system coercive functional $C$-condition. local linking indefinite linear part
DCDS
Two nontrivial solutions for periodic systems with indefinite linear part
D. Motreanu V. V. Motreanu Nikolaos S. Papageorgiou
We consider second order periodic systems with a nonsmooth potential and an indefinite linear part. We impose conditions under which the nonsmooth Euler functional is unbounded. Then using a nonsmooth variant of the reduction method and the nonsmooth local linking theorem, we establish the existence of at least two nontrivial solutions.
keywords: Second order periodic system PS-condition multiple solutions local linking. nonsmooth reduction method
CPAA
A unified treatment using critical point methods of the existence of multiple solutions for superlinear and sublinear Neumann problems
D. Motreanu Donal O'Regan Nikolaos S. Papageorgiou
In this paper we present a framework which permits the unified treatment of the existence of multiple solutions for superlinear and sublinear Neumann problems. Using critical point theory, truncation techniques, the method of upper-lower solutions, Morse theory and the invariance properties of the negative gradient flow, we show that the problem can have seven nontrivial smooth solutions, four of which have constant sign and three are nodal.
keywords: upper-lower solutions gradient flow truncation techniques multiple solutions. Morse theory Superlinear and sublinear problems critical point theory

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