We consider the nonlinear eigenvalue problem −div ( |∇u|∇u ) = λ|u|u in Ω, u = 0 on ∂Ω, where Ω is a bounded open set in R with smooth boundary and p, q are continuous functions on Ω such that 1 < infΩ q < infΩ p < supΩ q, supΩ p < N , and q(x) < Np(x)/ (N − p(x)) for all x ∈ Ω. The main result of this paper establishes that any λ > 0 sufficiently small is an eigenvalue of the above nonhomogene...

Like mechanics and electrodynamics, the fundamental laws of the thermodynamics of dissipative processes can be compressed into a variational principle. This variational principle both in its differential (local) and in integral (global) forms was formulated by Gyarmati helped by the present author in 1965. This principle was applied to several fields of irreversible processes: first of all, his...

In this paper we establish new forward and backward versions of Ekeland’s variational principle for the class of strictly-decreasing forward(resp. backward-) lower-semicontinuou functionals in pseudo-quasimetric spaces. We do not require that the space under consideration either is complete or enjoys the limit uniqueness property due to the fact that the collections of forward and backward limi...

The variational principle of barotropic Eulerian fluid dynamics is known to be quite cumbersome containing as much as eleven independent functions. This is much more than the the four functions (density and velocity) appearing in the Eulerian equations of motion. This fact may have discouraged applications of the variational method. In this paper a four function Eulerian variational principle i...

In this article we introduce a dual of the uniform boundedness principle which does not require completeness and gives an indirect means for testing set. The principle, although known to analyst despite its applications in establishing results such as Hellinger--Toeplitz theorem, is often missing from elementary treatments functional analysis. Example 1 indicate connection between question spir...

We establish the variational principle of Kolmogorov-PetrovskyPiskunov (KPP) front speeds in a one dimensional random drift which is a mean zero stationary ergodic process with mixing property and local Lipschitz continuity. To prove the variational principle, we use the path integral representation of solutions, hitting time and large deviation estimates of the associated stochastic flows. The...

h this paper, we use the auxiliary principle technique to suggest a new &ass of predictor-corrector algorithms for solving generalized variational inequalities. The convergence of the proposed method only requires the partially relaxed strongly monotonicity of the operator, which is weaker than co-coercivity. As special cases, we obtain a number of known and new results for solving va,rious cla...

This paper presents a numerical solution for vibration analysis of a cantilever trapezoidal thick plate. The material of the plate is considered to be graded through the thickness from a metal surface to a ceramic one according to a power law function. Kinetic and strain energies are derived based on the Reissner-Mindlin theory for thick plates and using Hamilton's principle, the governing equa...

As we will see during this talk, the Bayesian and information-theoretic views of variational inference provide complementary and mutually beneficial perspectives to the same problems with two different languages. More specifically, based on the paper by Honkela and Valpola [4], we will provide an interpretation of variational inference based on the MDL principle as a theoretical framework for m...

We introduce a variational principle suitable for the computational modeling of crystalline materials. We consider a class of materials that are described by non-quasiconvex variational integrals. We are further focused on equlibria of such materials that have non-attainment structure, i.e., Dirichlet boundary conditions prohibit these variational integrals from attaining their infima. Conseque...