Yazar "Ekincioglu, Ismail" seçeneğine göre listele

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    Approximating Functions in the Power-Type Weighted Variable Exponent Sobolev Space by the Hardy Averaging Operator
    (Univ Nis, Fac Sci Math, 2022) Ayazoglu, Rabil; Ekincioglu, Ismail; Sener, S. Sule
    We investigate the problem of approximating function f in the power-type weighted variable exponent Sobolev space W-alpha(.)(r,p(.)) (0, 1), (r = 1, 2,...), by the Hardy averaging operator A (f) (x) = 1/x integral(x)(0) f (t)dt. If the function f lies in the power-type weighted variable exponent Sobolev space W-alpha(.)(r,p(.)) (0, 1), it is shown that parallel to A(f) - f parallel to(p(.),alpha(.)-rp(.)) <= C parallel to f((r))parallel to(p(.),alpha(.)') where C is a positive constant. Moreover, we consider the problem of boundedness of Hardy averaging operator A in power-type weighted variable exponent grand Lebesgue spaces Lp(alpha(.))(p(.),theta) (0, 1). The sufficient criterion established on the power-type weight function alpha(.) and exponent p(.) for the Hardy averaging operator to be bounded in these spaces.
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    EXISTENCE OF ONE WEAK SOLUTION FOR p(x)-BIHARMONIC EQUATIONS INVOLVING A CONCAVE-CONVEX NONLINEARITY
    (Math Soc Serbia-Drustvo Matematicara Srbije, 2017) Ayazoglu (Mashiyev), Rabil; Alisoy, Gulizar; Ekincioglu, Ismail
    In the present paper, using variational approach and the theory of the variable exponent Lebesgue spaces, the existence of nontrivial weak solutions to a fourth order elliptic equation involvinga p(x)-biharmonic operator and a concave-convex nonlinearity the Navier boundary conditionsis obtained.
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    Lower bounds for blow-up time in a nonlinear parabolic problem with a gradient nonlinearity
    (Springer Heidelberg, 2022) Mashiyev, Rabil Ayazoglu; Ekincioglu, Ismail
    In this article, we study the blow-up properties of solutions to a parabolic problem with a gradient nonlinearity under homogeneous Dirichlet boundary conditions. By constructing an auxiliary function and by modifying the first order differential inequality, we obtain lower bounds for the blow-up time of solutions in L-k (Omega) (k > 1) norm and conditions which ensure that blow-up cannot occur.