Kanishka Perera

Nontrivial critical groups in

We construct and variationally characterize by a min-max procedure involving the Yang index a new sequence of eigenvalues of the

p

p

-Laplacian problems via the Yang index

-Laplacian, and use the structure provided by this sequence to show that the associated variational functional always has a nontrivial critical group. As an application we obtain nontrivial solutions for a class of

BASIC PROPERTIES OF SOBOLEV'S SPACES ON TIME SCALES

p

Homological local linking

-superlinear problems.

A generalization of the Amann-Zehnder theorem to nonresonance problems with jumping nonlinearities

We study the theory of Sobolevs spaces of functions defined on a closed subinterval of an arbitrary time scale endowed with the Lebesgue Δ-measure; analogous properties to that valid for Sobolevs spaces of functions defined on an arbitrary open interval of the real numbers are derived.

Solution of nonlinear equations having asymptotic limits at zero and infinity

We generalize the notion of local linking to include certain cases where the functional does not have a local splitting near the origin. Applications to second-order Hamiltonian systems are given.

The Fucik spectrum and critical groups

Abstract. We obtain nontrivial solutions of semilinear boundary value problems with jumping nonlinearities that interact with the Fucik spectrum.

Multiple Positive Solutions in the Sense of Distributions of Singular BVPs on Time Scales and an Application to Emden-Fowler Equations

Abstract. We obtain nontrivial solutions for semilinear elliptic boundary value problems having asymptotic limits both at zero and at infinity.

Nonlinear integral equations singular in the dependent variable

We compute critical groups of zero for variational functionals arising from semilinear elliptic boundary value problems with jumping nonlinearities when the asymptotic limits of the nonlinearity fall in certain parts of Type (II) regions between curves of the Fucik spectrum.