In this work, we study the existence of non-trivial multiple solutions for a class of quasilinear elliptic systems equipped with concave-convex nonlinearities and critical growth terms in bounded domains. By using the variational method, especially Nehari manifold and Palais-Smale condition, we prove the existence and multiplicity results of positive solutions.

The existence of non-trivial solutions X to matrix equations of the form F (X,A1,A2, · · · ,As) = G(X,A1,A2, · · · ,As) over the real numbers is investigated. Here F and G denote monomials in the (n × n)-matrix X = (xij) of variables together with (n × n)-matrices A1,A2, · · · ,As for s ≥ 1 and n ≥ 2 such that F and G have different total positive degrees in X. An example with s = 1 is given by...

This paper is concerned with the existence of two non-trivial weak solutions for a p(x)-Kirchho type problem by using the mountain pass theorem of Ambrosetti and Rabinowitz and Ekeland's variational principle and the theory of the variable exponent Sobolev spaces.

In this paper, we present soliton-like solutions of the non-linear complex Klein-Gordon systems in 1+1 dimensions. We will use polar representation to introduce three different soliton-like solutions including, complex kinks (anti-kinks), radiative profiles, and localized wave-packets. Complex kinks (anti-kinks) are topological objects with zero electrical charges. Radiative profiles are object...

In this article, we present a two-point boundary value problem with separated conditions for finite nabla fractional difference equation. First, construct an associated Green’s function as series of functions the help spectral theory, and obtain some its properties. Under suitable on nonlinear part equation, deduce two existence results considered by means Leray–Schauder fixed point theorems. W...