• The Pure and Applied Mathematics
• /
• v.16 no.2
• /
• pp.213-225
• /
• 2009

This paper deals with the existence of positive solutions for a kind of multi-point nonlinear fractional differential boundary value problem at resonance. Our main approach is different from the ones existed and our main ingredient is the Leggett-Williams norm-type theorem for coincidences due to O'Regan and Zima. The most interesting point is the acquisition of positive solutions for fractional differential boundary value problem at resonance. And an example is constructed to show that our result here is valid.

• Journal of the Chungcheong Mathematical Society
• /
• v.31 no.2
• /
• pp.255-268
• /
• 2018

We establish the existence and multiplicity of positive solutions to a coupled system of fractional order differential equations satisfying three-point boundary conditions by utilizing Avery-Henderson functional fixed point theorems and under suitable conditions.

• Korean Journal of Mathematics
• /
• v.18 no.1
• /
• pp.87-96
• /
• 2010

We consider the semilinear biharmonic equation with Dirichlet boundary condition. We give a theorem that there exist at least three nontrivial solutions for the semilinear biharmonic boundary value problem. We show this result by using the critical point theory, the finite dimensional reduction method and the shape of the graph of the corresponding functional on the finite reduction subspace.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.2
• /
• pp.411-422
• /
• 2010

By using the fixed point index theory, we investigate the existence of at least two positive solutions for p-Laplace equation with sign-changing nonlinear terms $(\varphi_p(u'))'+a(t)f(t,u(t),u'(t))=0$, subject to some boundary conditions. As an application, we also give an example to illustrate our results.

• Korean Journal of Mathematics
• /
• v.26 no.1
• /
• pp.9-21
• /
• 2018

We investigate existence and multiplicity of the solutions for elliptic boundary value problem with two singularities. We obtain one theorem which shows that there exists at least one nontrivial weak solution under some conditions on which the corresponding functional of the problem satisfies the Palais-Smale condition. We obtain this result by variational method and critical point theory.

• Journal of applied mathematics & informatics
• /
• v.33 no.3_4
• /
• pp.425-434
• /
• 2015

In this paper, a two-point fractional boundary value problem at resonance is considered. By using the coincidence degree theory some existence results of solutions are established.

• Korean Journal of Mathematics
• /
• v.20 no.3
• /
• pp.333-341
• /
• 2012

We investigate the number of solutions for the superlinear elliptic bifurcation problem with Dirichlet boundary condition. We get a theorem which shows the existence of at least $k$ weak solutions for the superlinear elliptic bifurcation problem with boundary value condition. We obtain this result by using the critical point theory induced from invariant linear subspace and the invariant functional.

• Journal of the Korean Mathematical Society
• /
• v.45 no.5
• /
• pp.1361-1378
• /
• 2008

This paper deals with the study of dichotomy and conditioning for two-point boundary value problems associated with first order matrix Lyapunov systems, with the help of Kronecker product of matrices. Further, we obtain close relationship between the stability bounds of the problem on one hand, and the growth behaviour of the fundamental matrix solution on the other hand.

• Journal of applied mathematics & informatics
• /
• v.27 no.3_4
• /
• pp.875-883
• /
• 2009

At least two positive solutions of a first-order periodic boundary value problem with impulse are obtained by establishing a new cone and the theorem of fixed point index. And at the end of this paper we give an example to illustrate the application of our main results.

• Journal of applied mathematics & informatics
• /
• v.28 no.3_4
• /
• pp.945-952
• /
• 2010

In this paper, existence criteria of one solution to a nonlinear first-order periodic boundary value problem of impulsive dynamic equation on time scales are obtained by using the well-known Schaefer fixed-point theorem.