10 papers
Variational and nonvariational solutions for double phase variable exponent problems
Mustafa Avci
In this article, we examine two double-phase variable exponent problems, each formulated within a distinct framework. The first problem is non-variational, as the nonlinear term ma…
Positive weak solutions of a double-phase variable exponent problem with a fractional-Hardy-type singular potential and superlinear nonlinearity
Mustafa Avci
In the present paper, we study a double-phase variable exponent problem which is set up within a variational framework including a singular potential of fractional-Hardy-type. We e…
On the existence, uniqueness and stability of solutions of SDEs with state-dependent variable exponent
Mustafa Avci
We study a time-inhomogeneous nonlinear SDE with drift and diffusion governed by state-dependent variable exponents. This framework generalizes models like the geometric Brownian m…
A Topological Approach to Singular Double-Phase Equations with Variable Exponents
Mustafa Avci
In the present paper, we study a singular double phase variable exponent Dirichlet problem in the setting of a new Musielak-Orlicz Sobolev space with the nonlinearity (the external…
Stochastic representation of solutions for the parabolic Cauchy problem with variable exponent coefficients
Mustafa Avci
In this work, we prove existence and uniqueness of a bounded viscosity solution for the Cauchy problem of degenerate parabolic equations with variable exponent coefficients. We con…
On the geometric Brownian motion with state-dependent variable exponent diffusion term
Mustafa Avci
We propose a new stochastic model involving state-dependent variable exponent which allows modeling of systems where noise intensity adapts to the current state. This ne…