Existence and multiplicity of solutions for a class of superlinear elliptic systems

Abstract

In this paper, we establish the existence and multiplicity of solutions for a class of superlinear elliptic systems without Ambrosetti and Rabinowitz growth condition. Our results are based on minimax methods in critical point theory.

On the weak solutions of an overdetermined system of nonlinear fractional partial integro-differential equations

“…The standard and typical approach to study the existence of solutions to the nonlinear fractional boundary value problems is the fixed point theory, see for example [1,4,16,35]. But, another well-developed, successful and recently more attracting method is the calculus of variation to investigate the existence of solutions to the differential equation with type of integer order and very recently fractional order, the readers are referred to [7,[11][12][13][17][18][19][20][21]32,33,36] and the references therein to attain more information about this approach.…”

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

“…The standard theory and typical for the study of the existence of solutions to the nonlinear fractional boundary value problems is the theory of the fixed point, (see Refs. [19][20][21][22]. But there is a recently developed, successful and attractive mathematical method for studying the existence of solutions to the differential equation in a correct sort order and fractional arrangement recently (see Refs.…”