this paper is concerned with a 2nth-order p-laplacian difference equation. by using the critical point method, we establish various sets of sufficient conditions for the nonexistence and existence of solutions for neumann boundary value problem and give some new results. results obtained successfully generalize and complement the existing ones.

We consider the multiplicity of nontrivial solutions of the following quasilinear elliptic system -div(|x|(-ap)|∇u|(p-2)∇u) + f₁(x)|u|(p-2) u = (α/(α + β))g(x)|u| (α-2) u|v| (β) + λh₁(x)|u| (γ-2) u + l₁(x), -div(|x|(-ap) |∇v| (p-2)∇v) + f₂(x)|v| (p-2) v = (β/(α + β))g(x)|v|(β-2) v|u|(α) + μh 2(x)|v|(γ-2)v + l 2(x), u(x) > 0, v(x) > 0, x ∈ ℝ(N), where λ, μ > 0, 1 < p < N, 1 < γ < p < α + β < p* ...

Abstract The aim of this paper is to examine the existence at least two distinct nontrivial solutions a Schrödinger-type problem involving nonlocal fractional $p(\cdot )$ p ( ⋅ ) -Laplacian with concave–convex nonlinearities when, in general, nonlinear term d...

Using Struwe’s “monotonicity trick” and the recent blow-up analysis of Ohtsuka and Suzuki, we prove the existence of mountain pass solutions to a mean field equation arising in two-dimensional turbulence.

In this paper, we are concerned with the following critical fractional Choquard equation$ (-\Delta)^{s}u + V(x)u = (\mathcal{K}_{\mu}*|u|^{2^{*}_{\mu,s}})|u|^{2^{*}_{\mu,s}-2}u, \ u \in D^{s,2}(\mathbb{R}^{N}), $where $ s\in (0,1) $, N\geq 3 \max\{N-4s, 0\}&lt;\mu&lt;N 2^{*}_{\mu,s} \frac{2N-\mu}{N-2s} V(x) is a potential function, and \mathcal{K}_{\mu} Riesz potential. first part of combining ...

In this work we prove the existence of mountain pass solution for a fractional boundary value problem given by tD T (0D α t u(t)) = f(t, u(t)), t ∈ [0, T ] u(0) = u(T ) = 0.