• Title/Summary/Keyword: existence of solution

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EXISTENCE OF POSITIVE SOLUTIONS FOR EIGENVALUE PROBLEMS OF SINGULAR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

  • Lee, Yong-Hoon;Lee, Jinsil
    • East Asian mathematical journal
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    • v.33 no.3
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    • pp.323-331
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    • 2017
  • In this paper, we consider the existence of positive solutions for eigenvalue problems of nonlinear fractional differential equations with singular weights. We give various conditions on f and apply Krasnoselskii's Cone Fixed Point Theorem. As a result, we obtain several existence and nonexistence results corresponding to ${\lambda}$ in certain intervals.

ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO 3D CONVECTIVE BRINKMAN-FORCHHEIMER EQUATIONS WITH FINITE DELAYS

  • Le, Thi Thuy
    • Communications of the Korean Mathematical Society
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    • v.36 no.3
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    • pp.527-548
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    • 2021
  • In this paper we prove the existence of global weak solutions, the exponential stability of a stationary solution and the existence of a global attractor for the three-dimensional convective Brinkman-Forchheimer equations with finite delay and fast growing nonlinearity in bounded domains with homogeneous Dirichlet boundary conditions.

EXISTENCE AND UNIQUENESS OF SQUARE-MEAN PSEUDO ALMOST AUTOMORPHIC SOLUTION FOR FRACTIONAL STOCHASTIC EVOLUTION EQUATIONS DRIVEN BY G-BROWNIAN MOTION

  • A.D. NAGARGOJE;V.C. BORKAR;R.A. MUNESHWAR
    • Journal of applied mathematics & informatics
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    • v.41 no.5
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    • pp.923-935
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    • 2023
  • In this paper, we will discuss existence of solution of square-mean pseudo almost automorphic solution for fractional stochastic evolution equations driven by G-Brownian motion which is given as c0D𝛼𝜌 Ψ𝜌 = 𝒜(𝜌)Ψ𝜌d𝜌 + 𝚽(𝜌, Ψ𝜌)d𝜌 + ϒ(𝜌, Ψ𝜌)d ⟨ℵ⟩𝜌 + χ(𝜌, Ψ𝜌)dℵ𝜌, 𝜌 ∈ R. Furthermore, we also prove that solution of the above equation is unique by using Lipschitz conditions and Cauchy-Schwartz inequality. Moreover, examples demonstrate the validity of the obtained main result and we obtain the solution for an equation, and proved that this solution is unique.

EXISTENCE AND GLOBAL EXPONENTIAL STABILITY OF A PERIODIC SOLUTION TO DISCRETE-TIME COHEN-GROSSBERG BAM NEURAL NETWORKS WITH DELAYS

  • Zhang, Zhengqiu;Wang, Liping
    • Journal of the Korean Mathematical Society
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    • v.48 no.4
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    • pp.727-747
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    • 2011
  • By employing coincidence degree theory and using Halanay-type inequality technique, a sufficient condition is given to guarantee the existence and global exponential stability of periodic solutions for the two-dimensional discrete-time Cohen-Grossberg BAM neural networks. Compared with the results in existing papers, in our result on the existence of periodic solution, the boundedness conditions on the activation are replaced with global Lipschitz conditions. In our result on the existence and global exponential stability of periodic solution, the assumptions in existing papers that the value of activation functions at zero is zero are removed.

EXISTENCE OF A POSITIVE SOLUTION TO INFINITE SEMIPOSITONE PROBLEMS

  • Eunkyung Ko
    • East Asian mathematical journal
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    • v.40 no.3
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    • pp.319-328
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    • 2024
  • We establish an existence result for a positive solution to the Schrödinger-type singular semipositone problem: $-{\Delta}u\,=\,V(x)u\,=\,{\lambda}{\frac{f(u)}{u^{\alpha}}}$ in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in ℝN , N > 2, λ ∈ ℝ is a positive parameter, V ∈ L(Ω), 0 < α < 1, f ∈ C([0, ∞), ℝ) with f(0) < 0. In particular, when ${\frac{f(s)}{s^{\alpha}}}$ is sublinear at infinity, we establish the existence of a positive solutions for λ ≫ 1. The proofs are mainly based on the sub and supersolution method. Further, we extend our existence result to infinite semipositone problems with mixed boundary conditions.

EXISTENCE OF SOLUTION OF NONLINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS IN GENERAL BANACH SPACES

  • Jeong, Jin-Gyo;Shin, Ki-Yeon
    • Communications of the Korean Mathematical Society
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    • v.11 no.4
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    • pp.1003-1013
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    • 1996
  • The existence of a bounded generalized solution on the real line for a nonlinear functional evolution problem of the type $$ (FDE) x'(t) + A(t,x_t)x(t) \ni 0, t \in R $$ in a general Banach spaces is considered. It is shown that (FDE) has a bounded generalized solution on the whole real line with well-known Crandall and Pazy's result and recent results of the functional differential equations involving the operator A(t).

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C-EXISTENCE FAMILY AND EXPONENTIAL FORMULA

  • Lee, Young S.
    • Korean Journal of Mathematics
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    • v.11 no.1
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    • pp.51-55
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    • 2003
  • In this paper, we show that an exponentially bounded mild C-existence family can be represented by the exponential formula.

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ALTERNATIVE PROOF OF EXISTENCE THEOREM FOR CERTAIN COMPETITION MODELS

  • Ahn, Inkyung
    • Journal of the Chungcheong Mathematical Society
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    • v.13 no.1
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    • pp.119-130
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    • 2000
  • We give alternative proof of the existence theorem for certain elliptic systems describing competing interactions with nonlinear di usion. The existence of positive solution depends on the sign of the principal eigenvalue of suitable operators of Schr$\ddot{o}$dinger type. If the sign of such operators are both positive, then system has a positive solution. The main tool employed is the fixed point index of compact operator on positive cones.

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