Existence of a Nontrivial Solution for a Class of Superquadratic Elliptic Problems

We consider the existence of a nontrivial solution for the Dirichlet boundary value problem -△u+a(x)u=g(x,u),in Ω u=0, on Ω We prove an abstract result on the existence of a critical point for the functional f on a Hilbert space via the local linking theorem. Different from the works in the literature, the new theorem is constructed under the(C)* condition instead of (PS)* condition.

Existence of solutions for elliptic equations without superquadraticity condition

By weakening or dropping the superquadraticity condition （SQC）, the existence of positive solutions for a class of elliptic equations is established. In particular, we deal with the asymptotieal linearities as well as the superlinear nonlinearities.

Nontrivial Solutions of Superquadratic Hamiltonian Systems with Lagrangian Boundary Conditionsand the L-index Theory

In this paper, the authors study the existence of nontrivial solutions for the Hamiltonian systems z（t） = J△↓H（t, z（t）） with Lagrangian boundary conditions, where ^H（t,z）=1/2（^B（t）z, z） ＋ ^H（t, z）,^B（t） is a semipositive symmetric continuous matrix and ^H（t, z） = satisfies a superquadratic condition at infinity. We also obtain a result about the L-index.

PARTIAL REGULARITY RESULT OF SUPERQUADRATIC ELLIPTIC SYSTEMS WITH DINI CONTINUOUS COEFFICIENTS

We consider the partial regularity for weak solutions to superquadratic elliptic systems with controllable growth condition, under the assumption of Dini continuous coefficients. The proof relies upon an iteration scheme of a decay estimate for a new type of excess functional. To establish the decay estimate, we use the technique of A-harmonic approximation and obtain a general criterion for a weak solution to be regular in the neighborhood of a given point. In particular, the proof yields directly the optimal H¨older exponent for the derivative of the weak solutions on the regular set.

THE EXISTENCE OF NONTRIVIAL SOLUTIONS OF HAMILTONIAN SYSTEMS WITH LAGRANGIAN BOUNDARY CONDITIONS

Some theorems are obtained for the existence of nontrivial solutions of Hamiltonian systems with Lagrangian boundary conditions by the minimax methods.

ON THE MINIMAL PERIOD FOR PERIODIC SOLUTION PROBLEM OF NONLINEAR HAMILTONIAN SYSTEMS

The author proves a sharper estimate on the minimal period for periodic solutions of autonomous second order Hamiltonian systems under precisely Rabinowitz' superquadratic condition.

Further Bounds for Hardy Type Differences

In this paper we define a functional as a difference between the right-hand side and lefthand side of the refined Boas type inequality using the notation of superquadratic and subquadratic functions and study its properties, such as exponential and logarithmic convexity. We also, state and prove improvements and reverses of new weighted Boas type inequalities. As a special case of our result we obtain improvements and reverses of the Hardy inequality and its dual inequality. We introduce new Cauchy type mean and prove monotonicity property of this mean.

HOMOCLINIC ORBITS FOR LAGRANGIAN SYSTEMS

The existence of at least two homoclinic orbits for Lagrangian system (LS) is proved, wherethe Lagrangian L(t,x,y) =1/2∑aij(x)yiyj-V(t, x), in which the potential V(t,x) is globallysurperquadratic in x and T-periodic in t. The Concentration-Compactness Lemma and Mini-max argument are used to prove the existences.

NUMERICAL CALCULATION OF LONDON-VAN DER WAALS ADHESION FORCE DISTRIBUTIONS FOR DIFFERENT SHAPED PARTICLES

A basic method to calculate van der Waals dispersion force distributions for submicron superquadric particles in particle-wall systems is presented. The force distribution is achieved by rotating particles through a large number of arbitrary spatial orientations, each time keeping constant the contact distance to the wall surface while calculating the dispersion force. To accomplish this, the use of 2D particle shape suffices, that is, through using an inter-dimensional function, which has been determined previously. A further development of the method within digital image analysis may lead to possible applications to forecasting the macroscopic properties of particle systems, for example, flowability, agglomeration behavior or dispersibility. For small ranges of superquadric particle shapes, each with a different size, the way from determining the inter-dimensional function up to applying image analysis is shown in an example.