Two solutions to Kirchhoff-type fourth-order implusive elastic beam equations

In this paper, the existence of two solutions for superlinear fourth-order impulsive elastic beam equations is obtained. We get two theorems via variational methods and corresponding two-critical-point theorems. Combining with the Newton-iterative method, an example is presented to illustrate the value of the obtained theorems.

On the existence of solutions of one-dimensional fourth-order equations

UDC 517.9 Using variational methods and critical point theorems, we prove the existence of nontrivial solutions for one-dimensional fourth-order equations. Multiplicity results are also pointed out.

Infinitely many solutions to boundary value problem for fractional differential equations

Variational methods and critical point theorems are used to discuss existence of infinitely many solutions to boundary value problem for fractional order differential equations where Riemann-Liouville fractional derivatives and Caputo fractional derivatives are used. An example is given to illustrate our result.

Variational analysis to fourth-order impulsive differential equations

Applying two critical point theorems, we prove the existence of atleast three solutions for a one-dimensional fourth-order impulsive differential equation with two real parameters.

On Homoclinic Solutions for First-Order Superquadratic Hamiltonian Systems with Spectrum Point Zero

The existence and multiplicity of homoclinic solutions for a class of first-order periodic Hamiltonian systems with spectrum point zero are obtained. The proof is based on two critical point theorems for strongly indefinite functionals. Some recent results are improved and extended.

EXISTENCE AND MULTIPLICITY OF NONTRIVIAL SOLUTIONS FOR DEGENERATE HEMIVARIATIONAL INEQUALITIES INVOLVING LERAY–LIONS TYPE OPERATOR WITH CRITICAL GROWTH

In this paper, we investigate a hemivariational inequality involving Leray–Lions type operator with critical growth. Some existence and multiple results are obtained through using the concentration compactness principle of P. L. Lions and some nonsmooth critical point theorems.