Q-Heung Choi

Multiplicity results on a nonlinear biharmonic equation

Let ω be a bounded open set in Rn with smooth boundary ϖω We are concerned with a fourth order semilinear elliptic boundary value problem Δ2u + cΔu = bu+ + s inω under Dirichlet boundary condition. We investigate the existence of solutions of the fourth order nonlinear equation (0.1) when the nonlinearity bu+ crosses eigenvalues of Δ2 + cΔ under Dirichlet boundary condition.

MULTIPLICITY OF SOLUTIONS AND SOURCE TERMS IN A FOURTH ORDER NONLINEAR ELLIPTIC EQUATION

Abstract The authors investigate relations between multiplicity of solutions and source terms of the fourth order nonlinear elliptic boundary value problem under Dirichlet boundary condition Δ 2 u + c Δ u = bu + + f in Ω, where Ω is a bounded open set in R n with smooth boundary and the nonlinearity bu + crosses eigenvalues of Δ 2 + c Δ. They investigate the relations when the source term is constant and when it is generated by two eigenfuntions.

Controllability of nonlinear neutral evolution integrodifferential systems

Sufficient conditions for controllability of nonlinear neutral evolution integrodifferential systems in a Banach space are established. The results are obtained by using the resolvent operators and the Schaefer fixed-point theorem. An application to partial integrodifferential equation is given.

Nontrivial Solutions of the Asymmetric Beam System with Jumping Nonlinear Terms

We investigate the existence of multiple nontrivial solutions for perturbations and of the beam system with Dirichlet boundary condition in , in , where , and are nonzero constants. Here is the beam operator in , and the nonlinearity crosses the eigenvalues of the beam operator.

Nonlinear biharmonic boundary value problem

We consider the nonlinear biharmonic equation with variable coefficient and polynomial growth nonlinearity and Dirichlet boundary condition. We get two theorems. One theorem says that there exists at least one bounded solution under some condition. The other one says that there exist at least two solutions, one of which is a bounded solution and the other of which has a large norm under some condition. We obtain this result by the variational method, generalized mountain pass geometry and the critical point theory of the associated functional.MSC:35J20, 35J25, 35Q72.

Critical Point Theory Applied to a Class of the Systems of the Superquadratic Wave Equations

We show the existence of a nontrivial solution for a class of the systems of the superquadratic nonlinear wave equations with Dirichlet boundary conditions and periodic conditions with a superquadratic nonlinear terms at infinity which have continuous derivatives. We approach the variational method and use the critical point theory which is the Linking Theorem for the strongly indefinite corresponding functional.

Fourth order elliptic boundary value problem with nonlinear term decaying at the origin

We consider the number of the weak solutions for some fourth order elliptic boundary value problem with bounded nonlinear term decaying at the origin. We get a theorem, which shows the existence of the bounded solution for this problem. We obtain this result by approaching the variational method and using the generalized mountain pass theorem for the fourth order elliptic problem with bounded nonlinear term.MSC:35J30, 35J40.

TOPOLOGICAL APPROACH FOR THE MULTIPLE SOLUTIONS OF THE NONLINEAR PARABOLIC PROBLEM WITH VARIABLE COEFFICIENT JUMPING NONLINEARITY

We get a theorem which shows that there exist at least two or three nontrivial weak solutions for the nonlinear parabolic boundary value problem with the variable coefficient jumping nonlinearity. We prove this theorem by restricting ourselves to the real Hilbert space. We obtain this result by approaching the topological method. We use the Leray-Schauder degree theory on the real Hilbert space.

EXISTENCE RESULTS FOR SEMILINEAR DIFFERENTIAL EQUATIONS

In this paper we prove the existence of mild solutions for semilinear dierential equations in a Banach space. The results are obtained by using the semigroup theory and the Schaefer fixed point theorem. An example is provided to illustrate the theory.

A semilinear beam equation with nonconstant loads

We investigate multiplicity of solutions u(x, t) for a piecewise linear perturbation −(bu+−au−) of the one-dimensional beam operator utt + uxxx under Dirichlet boundary condition on the interval (fr|Sol|π/2,π/2) π/2) and periodic codition on the vasible t. Our concern is to investigate multiplicity of solutions of the equation when the nonlinearity crosses finite eigenvalues and the source term is generated by two eigenfunctions.