DISCUSSION OF CRITICAL LOAD IN NONLINEAR STABILITY ANALYSIS AND SUGGESTION OF VARIATIONAL PRINCIPLE OF SOLVING CRITICAL LOADS

In this paper, a set of variational formulas of solving nonlinear instability critical loads are established from the viewpoint of variational principle. The paper shows that it is very convenient to solve nonlinear instability critical load by using the variational formulas suggested in this paper.

ON POSITIVE G-SYMMETRIC SOLUTIONS OF A WEIGHTED QUASILINEAR ELLIPTIC EQUATION WITH CRITICAL HARDY-SOBOLEV EXPONENT

In this paper, we are concerned with a weighted quasilinear elliptic equation involving critical Hardy-Sobolev exponent in a bounded G-symmetric domain. By using the symmetric criticality principle of Palais and variational method, we establish several existence and multiplicity results of positive G-symmetric solutions under certain appropriate hypotheses on the potential and the nonlinearity.

MULTIPLE SYMMETRIC RESULTS FOR A CLASS OF BIHARMONIC ELLIPTIC SYSTEMS WITH CRITICAL HOMOGENEOUS NONLINEARITY IN R^N

This paper is dedicated to studying the existence and multiplicity of symmetric solutions for a class of biharmonic elliptic systems with critical homogeneous nonlinearity in RN. By virtue of variational methods and the symmetric criticality principle of Palais, we establish several existence and multiplicity results of G-symmetric solutions under certain appropriate hypotheses on the parameters and the weighted functions.

Theoretical analysis on capillary adhesion of microsized plates with a substrate

The stiction of a thin plate induced by the capillary force has attracted much attention in the broad range of applications. A novel method is presented to calculate the capillary adhesion problem of the plate through analytical method. The expressions of the surface energy, the strain energy and the total potential energy of the plate-substrate system have been analyzed and delineated. By means of continuum mechanics and the principle of minimum potential energy, the governing equation of the plate with an arbitrary shape and the corresponding transversality boundary condition due to the moving bound have been derived. Then the critical adhesion radius of the circular plate has been solved according to the supplementary transversality condition. Thus the deflections of the plates are analytically calculated with different critical adhesion radii. The results may be beneficial to the engineering application and the micro/nanomeasurement.

Existence of Nontrivial Solutions for p-Laplacian Variational Inclusion Systems in R^N

The authors study the existence of nontrivial solutions to p-Laplacian variational inclusion systems where N ≥ 2, 2 ≤ p ≤ N and F ： R^2 →% is a locally Lipschitz function. Under some growth conditions on F, and by Mountain Pass Theorem and the principle of symmetric criticality, the existence of such solutions is guaranteed.

A Multiplicity Result for Some Integro-Differential Biharmonic Equation in R^4

In this paper, we prove the existence of at least two nontrivial solutions for some biharmonic elliptic equation involving an integral term. The nonlinear term exhibits an exponential growth at infinity. Our method consists of a combination between variational tools and iterative technique.