POSITIVE SOLUTIONS FOR A CLASS OF p(x)-LAPLACIAN PROBLEMS

Abstract

Abstract. We consider the system ⎧ ⎨ ⎩

On the sub-supersolution principle for p(x)-Laplacian equations

“…Far from being complete, we refer readers to [6,9,17] and references cited therein. For example, the regularity of weak solutions for differential equations with variable exponent was studied in [2,12], and existence of solutions for variable exponent problems was studied in a series of papers [1,4,5,14].…”

A Fibering Map Approach for a Laplacian System With Sign-Changing Weight Function

“…(E ( λ ) ) admits at least two positive solutions for λ ∈ (0, λ 0 ), has a positive solution for λ = λ 0 and no positive solution exists for λ > λ 0 . For more general cases, we refer the reader to Afrouzi-Ala-Kazemipoor [1], Ambrosetti-Azorezo-Peral [3], de Figueiredo-Gossez-Ubilla [13], EL Hamidi [15] and Wu [25], etc. Recently, in [25] the author has considered a semilinear scalar elliptic equation involving concave-convex nonlinearities and sign-changing weight function, and showed multiplicity results with respect to the parameter λ via the extraction of Palais-Smale sequences in the Nehari manifold, where for the definition of Nehari manifolds we refer the reader to Nehari [18] or Willem [23].…”