Criteria for strong and weak random attractors

The theory of random attractors has different notions of attraction, amongst them pullback attraction and weak attraction. We investigate necessary and sufficient conditions for the existence of pullback attractors as well as of weak attractors

Solutions of nonlinear nonhomogeneous Neumann and Dirichlet Problems

We consider nonlinear Neumann and Dirichlet problems driven by a nonhomogeneous differential operator and a Caratheodory reaction. Our framework incorporates p-Laplacian equations and equations with the(p,q)-differential operator and with the generalized p-mean curvature operator. Using variational methods, together with truncation and comparison techniques and Morse theory, we prove multiplicity theorems, producing three, five or six nontrivial smooth solutions, all with sign information

Galerkin approximations for nonlinear evolution inclusions

summary:In this paper we study the convergence properties of the Galerkin approximations to a nonlinear, nonautonomous evolution inclusion and use them to determine the structural properties of the solution set and establish the existence of periodic solutions. An example of a multivalued parabolic p.d.e\. is also worked out in detail

Nonlinear Dirichlet problems with a crossing reaction

We consider a nonlinear Dirichlet problem driven by the sum of a p-Laplacian (p \u3e 2) and a Laplacian, with a reaction that is (p-1)-sublinear and exhibits an asymmetric behavior near ∞ and -∞, crossing ^λ1 \u3e 0, the principal eigenvalue of (-Δp,W01,p(Ω)) (crossing nonlinearity). Resonance with respect to ^λ1(p) \u3e 0 can also occur. We prove two multiplicity results. The first for a Caratheodory reaction producing two nontrivial solutions and the second for a reaction C1 in the x-variable producing three nontrivial solutions. Our approach is variational and uses also the Morse theory

Prominent Australians : and importance of Camperdown cemetery, N.S.W.

cover-title.; Also available in an electronic version via the Internet at: http://nla.gov.au/nla.aus-vn1946495

Nonlinear Neumann equations driven by a nonhomogeneous differential operator

We consider a nonlinear Neumann problem driven by a nonhomogeneous nonlinear differential operator and with a reaction which is (p-1)-superlinear without necessarily satisfying the Ambrosetti-Rabinowitz condition. A particular case of our differential operator is the p-Laplacian. By combining variational methods based on critical point theory with truncation techniques and Morse theory, we show that the problem has at least three nontrivial smooth solutions, two of which have constant sign (one positive and the other negative)