Tacksun Jung

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.

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.

Elliptic system with some singular nonlinearity

Abstract We investigate multiplicity of solutions for elliptic systems with singular non-linearities. We obtain a theorem which shows that elliptic systems with some singular non-linearities have infinitely many solutions. We get this result by using the variational method, critical point theory and homology theory.

Weak solutions for the singular potential wave system

We investigate the existence of weak solutions for a class of the system of wave equations with singular potential nonlinearity. We obtain a theorem which shows the existence of nontrivial weak solution for a class of the wave system with singular potential nonlinearity and the Dirichlet boundary condition. We obtain this result by using the variational method and critical point theory for indefinite functional.MSC:35L51, 35L70.

Existence of four solutions for the elliptic problem with nonlinearity crossing one eigenvalue

We investigate the multiplicity of the weak solutions for the nonlinear elliptic boundary value problem. We get a theorem which shows the existence of at least four weak solutions for the asymptotically linear elliptic problem with Dirichlet boundary condition. We obtain this result by using the Leray-Schauder degree theory, the variational reduction method and critical point theory.MSC:35J15, 35J25.

At least three solutions for the Hamiltonian system and reduction method

We investigate the multiplicity of solutions for the Hamiltonian system with some asymptotically linear conditions. We get a theorem which shows the existence of at least three 2π-periodic solutions for the asymptotically linear Hamiltonian system. We obtain this result by the variational reduction method which reduces the infinite dimensional problem to the finite dimensional one. We also use the critical point theory and the variational method.MSC:35A15, 37K05.

Singular potential Hamiltonian system

We investigate multiple solutions for the Hamiltonian system with singular potential nonlinearity and periodic condition. We get a theorem which shows the existence of the nontrivial weak periodic solution for the Hamiltonian system with singular potential nonlinearity. We obtain this result by using the variational method, critical point theory for indefinite functional.MSC:35Q70.