In this paper we study a quasilinear elliptic system coupled by Schrödinger equation with p-Laplacian operator and Poisson equation. Some scaling transformation ingenious methods are applied to produce the bounded Palais-Smale sequences existence of nontrivial solutions for is obtained mountain pass theorem.

Aim of this work is to investigate existence and multiplicity positive solutions a fractional boundary value problem with an integral condition p-Laplacian operator. Necessary sufficient conditions are presented obtain results. Main tools Krasnoselskii, Schaefer Leggett-Williams fixed point theorems. Two examples given illustrate our

In this paper, we consider the nonlinear impulsive generalized fractional differential equations with (p,q)-Laplacian operator for 1<p≤q<∞, in which nonlinearity f contains two derivatives respect to another function. Since complexity of term and impulses exist calculus, it is difficult find corresponding variational functional problem. The existence nontrivial solutions problem establish...

In this work we introduce volume constraint problems involving the nonlocal operator $$(-\Delta )_{\delta }^{s}$$ , closely related to fractional Laplacian )^{s}$$ and depending upon a parameter $$\delta >0$$ called horizon. We study associated linear spectral behavior of these when \rightarrow 0^+$$ +\infty $$ . Through limit processes on derive convergence local as respectively, well prove so...

We consider the boundary value problem −ψ(x, u(x), u′(x))′ = f(x, u(x), u′(x)), a.e. x ∈ (0, 1), (1) c00u(0) = c01u ′(0), c10u(1) = c11u ′(1), (2) where |cj0| + |cj1| > 0, for each j = 0, 1, and ψ, f : [0, 1] × R2 → R are Carathéodory functions, with suitable additional properties. The differential operator generated by the left-hand side of (1), together with the boundary conditions (2), is a ...

In this paper we study the asymptotic behavior of the ground state energy E(R) of the Schrödinger operator PR = −∆ + V1(x) + V2(x−R), x, R ∈ IR, where the potentials Vi are small perturbations of the Laplacian in IR, n ≥ 3. The methods presented here apply also in the investigation of the ground state energy E(g) of the operator Pg = P + V1(x) + V2(gx), x ∈ X, g ∈ G, where Pg is an elliptic ope...

is a vector version of p-Laplacian operator. In order to say what we understand by solution for the problem (1.1), (1.2) we remind some basic results concerning the W 1,p T -spaces. Let C T be the space of indefinitely differentiable T -periodic functions from R to R . We denote by 〈·, ·〉 the inner product on R and by ‖ · ‖, the norm generated by this inner product (the same meaning is applied ...