Existence of Weak Solutions for a New Class of Fractional p-Laplacian Boundary Value Systems

Abstract

In this paper, at least three weak solutions were obtained for a new class of dual non-linear dual-Laplace systems according to two parameters by using variational methods combined with a critical point theory due to Bonano and Marano. Two examples are given to illustrate our main results applications.

Existence of 3-Weak Solutions for a New Class of an Overdetermined System of Fractional Partial Integro-Differential Equations

“…for example, see (Refs. 7,(13)(14)(15)(19)(20)23,32,(34)(35)(36)(37). Moreover, recently, the existence of solutions of boundary value problems for Fractional differential equations have widely been studied in many papers and we refer the reader to Refs.…”

On Existence of Sequences of Weak Solutions of Fractional Systems with Lipschitz Nonlinearity

“…More and more efforts have been made in the fractional calculus field especially in FDEs (see, for instance, [2,5,[8][9][10][11][12][13][14][27][28][29][30][31][32][33][34][35][36][37][38][39]). Solution existence for a lot of boundary value problems and several nonlinear elementary problems is studied via a huge number of techniques and nonlinear mathematical tools (see [7,[15][16][17][18][19][20][21][22][23]): the theory of critical point, fixed-point theory, technique of monochromatic iterative, theory degree of coincidence, and the change methods. Motivated by multiple works involved in this domain, we concentrate in this paper on the existence of several infinite solutions to the following fractional-order differentiation system:…”

“…In the last few months, we treated the same area of this study, in [18], by using variational methods together with a critical point theory due to Bonano and Marano. We got at least three weak solutions for the following nonlinear dual-Laplace systems with respect to two parameters:…”

Multiplicity Solutions of Fractional Impulsive p -Laplacian Systems: New Result

“…In viscoelasticity, electrochemistry, power, porous media, and electromagnetism, for instance, see and the references therein. Many articles have recently investigated the existence of solutions to boundary value problems for FDEs, and we refer the reader to one of them [2,[18][19][20][34][35][36][37][38][39][40][41][42][43][44][45][46] and the references therein. For example, Kamache et al [40] investigated the existence of three solutions for a class of fractional p-Laplacian systems using a variational structure and critical point theory.…”