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DCDS

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.

CPAA

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

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.

CPAA

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.

## Year of publication

## Related Authors

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