PERIODIC SYSTEMS WITH TIME DEPENDENT MAXIMAL MONOTONE OPERATORS

We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the convex and nonconvex problems.We also show the existence of extremal periodic solutions and provide a strong relaxation theorem.Finally,we provide an application to nonlinear periodic control systems.

SINGULAR DOUBLE PHASE EQUATIONS

We study a double phase Dirichlet problem with a reaction that has a parametric singular term. Using the Nehari manifold method, we show that for all small values of the parameter, the problem has at least two positive, energy minimizing solutions.

MULTIPLE SOLUTIONS FOR NONAUTONOMOUS SECOND ORDER PERIODIC SYSTEMS

We study nonautonomonus second order periodic systems with a nonslnooth potential. Using the nonsmooth critical theory, we establish the existence of at least two nontrivial solutions. Our framework incorporates large classes of both subquadratic and superquadratic potentials at infinity.

LANDESMAN-LAZER TYPE (p,q)-EQUATIONS WITH NEUMANN CONDITION

We consider a Neumann problem driven by the(p,g)-Laplacian under the Landesman-Lazer type condition.Using the classical saddle point theorem and other classical results of the calculus of variations,we show that the problem has at least one nontrivial weak solution.

SEMILINEAR HEMIVARIATIONAL INEQUALITIES WITH STRONG RESONANCE AT INFINITY

A semilinear elliptic equation with strong resonance at infinity and with a nonsmooth potential is studied. Using nonsmooth critical point theory and developing some abstract minimax principles which complement and extend results in the literature, two results on existence are obtained.

ON NONLINEAR ELLIPTIC HEMIVARIATIONAL INEQUALITIES OF SECOND ORDER

In this paper, a nonlinear hemivariational inequality of second order with a forcing term of subcritical growth is studied. Using techniques from multivalued analysis and the theory of nonlinear operators of monotone type, an existence theorem for the Dirichlet boundary value problem is proved.

POSITIVE SOLUTIONS FOR PARAMETRIC EQUIDIFFUSIVE p-LAPLACIAN EQUATIONS

We consider a parametric Dirichlet problem driven by the p-Laplacian with a Caratheodory reaction of equidiffusive type. Our hypotheses incorporate as a special case the equidiffusive p-logistic equation. We show that if λ1 〉 0 is the principal eigenvalue of the Dirichlet negative p-Laplacian and ）λ 〉 λ1 （/k being the parameter）, the problem has a unique positive solution, while for ）λ ∈ （0, λ1], the problem has no positive solution.

ON NONCOERCIVE (p,q)-EQUATIONS

We consider a nonlinear Dirichlet problem driven by a(p,q)-Laplace differential operator(1<q<p).The reaction is(p-1)-linear near±∞and the problem is noncoercive.Using variational tools and truncation and comparison techniques together with critical groups,we produce five nontrivial smooth solutions all with sign information and ordered.In the particular case when q=2,we produce a second nodal solution for a total of six nontrivial smooth solutions all with sign information.

ARBITRARILY SMALL NODAL SOLUTIONS FOR PARAMETRIC ROBIN(p,q)-EQUATIONS PLUS AN INDEFINITE POTENTIAL

We consider a nonlinear Robin problem driven by the(p,q)-Laplacian plus an indefinite potential term and with a parametric reaction term.Under minimal conditions on the reaction function,which concern only its behavior near zero,we show that,for all λ>0 small,the problem has a nodal solution y_(λ)∈C^(1)(Ω)and we have y_(λ)→0 in C^(1)(Ω)asλ→0^(+).

ANISOTROPIC(p,q)-EQUATIONS WITH COMPETITION PHENOMENA

We consider a nonlinear Robin problem driven by the anisotropic(p,q)-Laplacian and with a reaction exhibiting the competing effects of a parametric sublinear(concave) term and of a superlinear(convex) term.We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter varies.We also prove the existence of a minimal positive solution and determine the monotonicity and continuity properties of the minimal solution map.

Resonant-Superlinear Nonhomogeneous Dirichlet Problems

We consider a Dirichlet nonlinear equation driven by the(p,2)-Laplacian and with a reaction having the competing effects of a parametric asymmetric superlinear term and a resonant perturbation.We show that for all small values of the parameter the problem has at least five nontrivial smooth solutions all with sign information.

Parametric Anisotropic(p,q)-Neumann Problems

We consider a Neumann problem driven by a(p(z), q(z))-Laplacian(anisotropic problem) plus a parametric potential term with λ > 0 being the parameter. The reaction is superlinear but need not satisfy the Ambrosetti-Rabinowitz condition. We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter λ moves on R_(+)=(0,+∞).

Existence Theorems for Periodic Differential Inclusions in IR^N

We study the periodic problem for differential inclusions in R^N.First we look for extremal periodicsolutions.Using techniques from multivalued analysis and a fixed point argument we establish an existencetheorem under some general hypotheses.We also consider the“nonconvex periodic problem”under lowersemicontinuity hypotheses,and the“convex periodic problem”under general upper semicontinuity hypotheseson the multivalued vector field.For both problems,we prove existence theorems under very general hypotheses.Our approach extends existing results in the literature and appear to be the most general results on the nonconvexperiodic problem.