• Title/Summary/Keyword: mixed type functional equation

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Some Nonlinear Alternatives in Banach Algebras with Applications II

  • Dhage, B.C.
    • Kyungpook Mathematical Journal
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    • v.45 no.2
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    • pp.281-292
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    • 2005
  • In this paper a nonlinear alternative of Leray-Schauder type is proved in a Banach algebra involving three operators and it is further applied to a functional nonlinear integral equation of mixed type $$x(t)=k(t,x({\mu}(t)))+[f(t,x({\theta}(t)))]\(q(t)+{\int}_0{^{\sigma}^{(t)}}v(t,s)g(s,x({\eta}\(s)))ds\)$$ for proving the existence results in Banach algebras under generalized Lipschitz and $Carath{\acute{e}}odory$ conditions.

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A FIXED POINT APPROACH TO THE ORTHOGONAL STABILITY OF MIXED TYPE FUNCTIONAL EQUATIONS

  • JEON, YOUNG JU;KIM, CHANG IL
    • East Asian mathematical journal
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    • v.31 no.5
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    • pp.627-634
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    • 2015
  • In this paper, we investigate the following orthogonally additive-quadratic functional equation f(2x + y) - f(x + 2y) - f(x + y) - f(y - x) - f(x) + f(y) + f(2y) = 0. and prove the generalized Hyers-Ulam stability for it in orthogonality spaces by using the fixed point method.

ON THE STABILITY OF A MIXED TYPE FUNCTIONAL EQUATION

  • Lee, Sang-Baek;Park, Won-Gil;Bae, Jae-Hyeong
    • Journal of the Chungcheong Mathematical Society
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    • v.19 no.1
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    • pp.69-77
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    • 2006
  • The generalized Hyers-Ulam stability problems of the mixed type functional equation $$f\({\sum_{i=1}^{4}xi\)+\sum_{1{\leq}i<j{\leq}4}f(x_i+x_j)=\sum_{i=1}^{4}f(x_i)+\sum_{1{\leq}i<j<k{\leq}4}f(x_i+X_j+x_k)$$ is treated under the approximately even(or odd) condition and the behavior of the quadratic mappings and the additive mappings is investigated.

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MULTIPLE SOLUTIONS RESULT FOR THE MIXED TYPE NONLINEAR ELLIPTIC PROBLEM

  • Jung, Tacksun;Choi, Q-Heung
    • Korean Journal of Mathematics
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    • v.19 no.4
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    • pp.423-436
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    • 2011
  • We obtain a theorem that shows the existence of multiple solutions for the mixed type nonlinear elliptic equation with Dirichlet boundary condition. Here the nonlinear part contain the jumping nonlinearity and the subcritical growth nonlinearity. We first show the existence of a positive solution and next find the second nontrivial solution by applying the variational method and the mountain pass method in the critical point theory. By investigating that the functional I satisfies the mountain pass geometry we show the existence of at least two nontrivial solutions for the equation.

EXISTENCE OF THREE WEAK SOLUTIONS FOR A CLASS OF NONLINEAR OPERATORS INVOLVING p(x)-LAPLACIAN WITH MIXED BOUNDARY CONDITIONS

  • Aramaki, Junichi
    • Nonlinear Functional Analysis and Applications
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    • v.26 no.3
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    • pp.531-551
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    • 2021
  • In this paper, we consider a mixed boundary value problem to a class of nonlinear operators containing p(x)-Laplacian. More precisely, we consider the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary. We show the existence of at least three weak solutions under some hypotheses on given functions and the values of parameters.