• 대한수학회지
• /
• 제39권3호
• /
• pp.439-460
• /
• 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.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제2권1호
• /
• pp.1-14
• /
• 1998

Multiplicity results of doubly-periodic solution for semilinear heat equations having coercive nonlinearity are discussed. Our proofs rely on Mawhin's continuation theorem.

• 대한수학회지
• /
• 제36권2호
• /
• pp.355-367
• /
• 1999

We prove the existence of 2N-1 distinct ordered positive solutions of a class of semilinear elliptic Dirichlet boundary value problems on Rn when the forcing term has N distinct positive stable zeros and the coefficient function decaying to the zero at infinity.

• 대한수학회지
• /
• 제56권5호
• /
• pp.1309-1331
• /
• 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
• /
• 제38권1호
• /
• pp.13-20
• /
• 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.

• 대한수학회지
• /
• 제45권6호
• /
• pp.1549-1559
• /
• 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.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1997년도 한국자동제어학술회의논문집; 한국전력공사 서울연수원; 17-18 Oct. 1997
• /
• pp.309-312
• /
• 1997

The dynamic characteristics of a continuous MMA/MA free-radical solution copolymerization reactor were studied. A mathematical model was developed and kinetic parameters which had been estimated in the previous work were used. With this model, bifurcation diagrams were constructed with various parameters as the bifurcation parameter to predict the region of stable operating conditions and to enhance the controller performance. It was shown that the steady-state multiplicity existed over wide ranges of residence time and jacket inlet temperature. Periodic solution branches were found to emanated from Hopf bifurcation points. Under certain conditions isola was also observed, which would result in poor performance of feedback controllers.

• International Journal of Computer Science & Network Security
• /
• 제21권6호
• /
• pp.127-136
• /
• 2021

In the systems and software modeling field, a conceptual model involves modeling with concepts to support development and design. An example of a conceptual model is a description developed using the Unified Modeling Language (UML). UML uses a model multiplicity formulation approach, wherein a number of models are used to represent alternative views. By contrast, a model singularity approach uses only a single integrated model. Each of these styles of modeling has its strengths and weaknesses. This paper introduces a partial solution to the issue of multiplicity vs. singularity in modeling by adopting UML use cases and class models into the conceptual thinging machine (TM) model. To apply use cases, we adopt the observation that a use-case diagram is a description that shows the internal structure of the part of the system represented by the use case in addition to being useful to people outside of the system. Additionally, the UML class diagram is recast in TM representation. Accordingly, we develop a TMUML model that embraces the TM specification of the UML class diagram and the internal structure extracted from the UML use case. TMUML modeling introduces some of the advantages that have made UML a popular modeling language to TM modeling. At the same time, this approach supplies UML with partial model singularity. The paper details experimentation with TMUML using examples from the literature. Our results indicate that mixing UML with other models could be a viable approach.

• East Asian mathematical journal
• /
• 제38권5호
• /
• pp.593-601
• /
• 2022

In this paper, we consider singular 𝜑-Laplacian problems with nonlocal boundary conditions. Using a fixed point index theorem on a suitable cone, the existence results for one or two positive solutions are established under the assumption that the nonlinearity may not satisfy the L¹-Carathéodory condition.

• Journal of applied mathematics & informatics
• /
• 제35권1_2호
• /
• pp.11-24
• /
• 2017

Using variational methods, we study the existence and multiplicity of weak solutions for some p(x)-Laplacian-like problems. First, without assuming any asymptotic condition neither at zero nor at infinity, we prove the existence of a non-zero solution for our problem. Next, we obtain the existence of two solutions, assuming only the classical Ambrosetti-Rabinowitz condition. Finally, we present a three solutions existence result under appropriate condition on the potential F.