• Journal of the Korean Mathematical Society
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• v.38 no.4
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• pp.853-881
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• 2001

Multiplicity for doubly-periodic solutions and Dirichlet-Periodic solutions are treated.

• Bulletin of the Korean Mathematical Society
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• v.37 no.4
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• pp.697-710
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• 2000

We investigate the existence of solutions of the nonlinear heat equation under Dirichlet boundary conditions on $\Omega$ and periodic condition on the variable t, $Lu-D_tu$+g(u)=f(x, t). We also investigate a relation between multiplicity of solutions and the source terms of the equation.

• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.191-202
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• 2005

A condition on forcing term insuring the multiplicity of Dirichlet-periodic solutions of nonlinear dissipative hyperbolic equations is discussed. The nonlinear term is assumed to have coercive growth.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1309-1331
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• 2019

We study the homogeneous Dirichlet boundary value problem of generalized Laplacian systems with a singular weight which may not be in $L^1$. Using the well-known fixed point theorem on cones, we obtain the multiplicity results of positive solutions under two different asymptotic behaviors of the nonlinearities at 0 and ${\infty}$. Furthermore, a global result of positive solutions for one special case with respect to a parameter is also obtained.

• East Asian mathematical journal
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• v.38 no.1
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• pp.13-20
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• 2022

We establish multiplicity results for positive solutions to the Schrödinger-type singular positone problem: -∆u + V (x)u = λf(u) in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in ℝ^N, N > 2, λ is a positive parameter, V ∈ L^∞(Ω) and f : [0, ∞) → (0, ∞) is a continuous function. In particular, when f is sublinear at infinity we discuss the existence of at least three positive solutions for a certain range of λ. The proofs are mainly based on the sub- and supersolution method.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.735-749
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• 2000

The multiplicity if periodic sloutions of semilinear dissipative hyperbolic equations is treated

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.2
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• pp.1-6
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• 2001

Multiplicity of nonlinear second order nonlinear ordinary differential equations will be discussed.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1549-1559
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• 2008

In this paper, the existence and multiplicity of solution of periodic solutions of p-Laplacian boundary value problem are studied by using degree theory and upper and lower solutions method. Some known results are improved.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.943-956
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• 2000

We investigate a relation between multiplicity of solutions and source terms of jumping problem in wave equation when the nonlinearity crosses an eigenvalue and the source term is generated by finite eigenfunctions. We also show that the jumping problem has infinitely many solutions when the source term is positive multiple of the positve eigenfunction.

• Journal of the Korean Mathematical Society
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• v.39 no.3
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• pp.439-460
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• 2002

We prove the multiplicity of ordered positive radial solutions for a semilinear elliptic problem defined on an exterior domain. The key argument is to prove the existence of the third solution in presence of two known solutions. For this, we obtain some partial results related to three solutions theorem for certain singular boundary value problems. Proof are mainly based on the upper and lower solutions method and degree theory.