Ayazoglu, Rabil; Ekincioglu, Ismail

This paper deals with the following competitive two-species chemotaxis system with two chemicals with a source term of logistic type ut=Δu−χ1∇⋅(u∇υ)+η1u−μ1u2, υt=Δυ−υ+ω, ωt=Δω−χ2∇⋅(ω∇z)+η2ω−μ2ω2, 0=Δz−z+u, (x,t)∈Ω×(0,T) under homogeneous Neumann boundary conditions [Formula presented] and initial conditions u(x,0)=u0(x), υ(x,0)=υ0(x), ω(x,0)=ω0(x), x∈Ω, in a bounded domain Ω⊂RN (N≥1), where the parameters χ1, μ1, μ2>0 and η1, η2, χ2∈R. It is proved that the corresponding initial-boundary value problem possesses a unique global bounded classical solution if one of the following cases holds: (i)χ2≤0, (ii)χ2>0 as well as μ2 is large enough, which partially improves the results of [25].

AtıfScopus2·WoS2·OpenAlex2

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Ayazoglu Mashiyev, Rabil; 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 Lk(Ω ) (k> 1 ) norm and conditions which ensure that blow-up cannot occur.

İncele

Ayazoglu, Rabil; Ekincioglu, Ismail; Şener, S. Şule

We investigate the problem of approximating function f in the power-type weighted variable exponent Sobolev space (Formula presented), by the Hardy averaging operator (Formula presented). If α(.) x 0 the function f lies in the power-type weighted variable exponent Sobolev space (Formula presented) (0, 1), it is shown that (Formula presented), 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 (Formula presented) (0, 1). The sufficient α(.) criterion established on the power-type weight function α(.) and exponent p(.) for the Hardy averaging operator to be bounded in these spaces.

AtıfScopus3·WoS4·OpenAlex3

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Mashiyev, Rabil Ayazoglu; Alisoy, Gülizar; 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 involving a p(x)-biharmonic operator and a concave-convex nonlinearity the Navier boundary conditions is obtained.

AtıfScopus10

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Ayazoglu Mashiyev, Rabil; Ekincioglu, Ismail; Alisoy, Gulizar

In this paper, we deal with the following p(x)-Schrödinger problem: (Formula Presented) where the nonlinearity is sublinear. We present the existence of infinitely many solutions for the problem. The main tool used here is a variational method and Krasnoselskii’s genus theory combined with the theory of variable exponent Sobolev spaces. We also establish a Bartsch-Wang type compact embedding theorem for the variable exponent spaces.

AtıfScopus7·WoS7·OpenAlex4

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Mashiyev, R. Ayazoglu; Ekincioglu, Ismail

This article deals with a quasilinear elliptic equation with variable exponent under a homogenous Dirichlet boundary-value condition, where nonlinearity also depends on the gradient of the solution. By using an iterative method based on Mountain Pass techniques, the existence of a positive solution is obtained.

AtıfScopus11·WoS10·OpenAlex13

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