In this paper we consider second order differential inclusions in real Hilbert space, namely p(t) · x (t) + r(t) · x (t) ∈ Ax(t) + F (t, x(t)), a.e. on [0, T ], under the nonlinear boundary conditions. Using techniques from multivalued analysis and the theory of operators of monotone type, we prove the existence of solutions for both the 'convex' and 'nonconvex' problems. Finally, we present a special case of interest, which fit into our framework, illustrating the generality of our results. 2004 Elsevier Inc. All rights reserved.
Our aim in this paper is to study the initial boundary problem for the two-dimensional Kirchhoff type wave equation with an exponentially growing source term. We first prove that the Kirchhoff wave model is globally well-posed in (H01(Ω)∩L∞(Ω))×L2(Ω), which covers the case of degenerate stiffness coefficient, and then obtain that the semigroup generated by the problem has a global attractor in the corresponding phase space. We also point out that the above results are still true in the natural energy space H01(Ω)×L2(Ω).
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.