Unbalanced (p,2)-fractional problems with critical growth

Abstract

We study the existence, multiplicity and regularity results of non-negative solutions of following doubly nonlocal problem:where Ω ⊂ R n is a bounded domain with C 2 boundary ∂Ω, 0 < s 2 < s 1 < 1, n > 2s 1 , 1 < q < p < 2, 1 < r ≤ 2 * µ with 2 * µ = 2n−µ n−2s1 , λ, β > 0 and a ∈ L d d−q (Ω), for some q < d < 2 * s1 := 2n n−2s1 , is a sign changing function. We prove that each nonnegative weak solution of (P λ ) is bounded. Furthermore, we obtain some existence and multiplicity results using Nehari manifold method.

Multiple positive solutions for degenerate Kirchhoff equations with singular and Choquard nonlinearity

“…We define the following open convex subset of C ϕ (Ω) as Let ϕ 1 be the first positive normalized eigen‐function of (− Δ) s in X 0 . From [ 30, Proposition 1.1, Theorem 1.2] we recall that . Next we will show that the solutions of ( P λ ) are bounded and Hölder continuous in the case μ < 4 s .…”

2-Absorbing Intuitionistic Fuzzy Ideals of Commutative Semirings

“…In various ways, Badawi improved the research on these ideas in [5] and [2]. This notion was thoroughly studied by a number of additional researchers (see [6][7][8]).…”