Nonlinear elliptic problems involving the generalized p(u)-Laplacian operator with Fourier boundary condition

Abstract

This paper considers the existence of entropy solutions for some generalized elliptic p(u)-Laplacian problem with Fourier boundary conditions, when the variable exponent p is a real continuous function and we have dependency on the solution u. We get the results by assuming the right-hand sidefunction f to be an integrable function, and by using the regularization approach combined with the theoryof Sobolev spaces with variable exponents.

Novel Exploration of Topological Degree Method for Non-Instantaneous Impulsive Fractional Integro-Differential Equation through Application of Filtering System

“…Remark 3.7 One can observe that the above existence and uniqueness results (see theorems (3.5) and (3.6)) are based on the Ξ− Lipschitz, Ξ− condensing, TDM and Grownwall's inequality. This method is help to prove our result using weaker conditions instead of stronger conditions [3], [4], [8], [9], and [21]. The assumptions (P1)(ii) and (P2)(ii) are satisfied the equation ( 13) then by using the theorems (3.3) and (3.5), we can say the equation ( 13) has a solution on C(ℑ, R n ).…”

“…In recent years, many authors have studied the topological degree method for Caputo fractional differential equations as referred to in the dissertations [3], [4], [5], [8], and [17]. According to this fact, we will prove the TDM of non-instantaneous impulsive fractional integral-differential equations (NIFrIDE) with the Kuratowski measure of a non-compactness operator.…”