The purpose of this paper is to investigate the existence of three different weak solutions to a nonlinear elliptic problem that is governed by the weighted phi-Laplacian operator and subjected to Dirichlet boundary conditions. We also examine the presence of sequences of variational eigenvalues in two distinct scenarios, one with and one without assuming the Delta(2)-condition. Our main results are obtained through technical proofs that combine a Lagrange multipliers type approach with the Ljusternik-Schnirelmann argument.
In this paper, we not only show that the weak homogeneous Sobolev space W-.(alpha,p,infinity ) interpolates W-center dot(alpha,p) and BM(.)O(alpha,)but also propose the (BV, W-.a,W-p,W-infinity)-based model for image decomposition, thereby validating the interpolation inequality.
In this paper, we prove the existence of nontrivial solutions and multiple solutions for a specific class of p(x)-biharmonic system with Hardy potential and indefinite weight. Our major techniques incorporated variational approaches and several critical point theorems.
This paper is devoted to an intensive investigation of the major geometric aspects of the so-called (1, infinity) is not an element of p-harmonic capacitances within mathematical physics living on the Euclidean space & Ropf;(n >= 2).
The problem of decentralized guaranteed cost control for fractional-order interconnected time delay systems is considered in this paper. The design of guaranteed cost controllers is first proposed based on mathematical transformations with fractional calculus. A new sufficient condition in terms of linear matrix inequalities for the existence of decentralized guaranteed cost control for the interconnected fractional-order systems is derived. An example is provided to validate the correctness of the obtained theoretical results. Although there are some interesting methods for the design of guaranteed cost control laws for large-scale systems with integer order, they cannot be applied directly to fractional-order large-scale systems with time delays, since the Leibniz rule is not satisfied for fractional-order differentiation. Thus, designing a decentralized guaranteed cost control for fractional-order large-scale systems with time delays has been an open problem. The fractional-order Razumikhin theorem and mathematical transformations have been used to solve the decentralized guaranteed cost control for interconnected fractional-order systems with time-varying delays. The advantage of our approach is that it not only ensures that the controlled large-scale systems are asymptotically stable, but it also guarantees an adequate level of performance.
