In this paper, we study a class of integral boundary value problems for nonlinear differential equations of fractional order with p-Laplacian operator. Under some suitable assumptions, a new result on the existence of solutions is obtained by using a standard fixed point theorem. An example is included to show the applicability of our result.

We study the behavior of p-Dirichlet optimal design problem with volume constraint for p large. As the limit as p goes to infinity, we find a limiting free boundary problem governed by the infinity-Laplacian operator. We establish a necessary and sufficient condition for uniqueness of the limiting problem and, under such a condition, we determine precisely the optimal configuration for the limi...

This paper deals with the homogenization of a one-dimensional nonlinear non-local variable index p(x)-Laplacian operator Lɛ periodic structure and convolution kernel. By constructing scale diffusive model two corrector functions χ1 χ2, as parameter ɛ → 0+, we first obtain that limit L is p-Laplacian constant exponent coefficients such Lu=Rddx(|u′(x)|p−2u′(x)). Then, for given function f∈Lq(R)(q...

The operator square root of the Laplacian (−△) can be obtained from the harmonic extension problem to the upper half space as the operator that maps the Dirichlet boundary condition to the Neumann condition. In this paper we obtain similar characterizations for general fractional powers of the Laplacian and other integro-differential operators. From those characterizations we derive some proper...

This paper concerned with the existence of solutions of anti-periodic boundary value problems for impulsive differential equations with φ-Laplacian operator. Firstly, the definition a pair of coupled lower and upper solutions of the problem is introduced. Then, under the approach of coupled upper and lower solutions together with Nagumo condition, we prove that there exists at least one solutio...

In this paper we study a nonlinear boundary eigenvalue problema governed by the one-dimensional p-Laplacian operator with impulse, give some properties of first λ1 and prove existence eigenvalues sequence {λn}n∈N∗ using Lusternik-Schnirelman principle, as well characterization eigenvalues, discuss strict monotonicity that eigenfunction corresponding to second λ2 changes sign only once on [0, 1].

where D , D , and D are the standard Riemann-Liouville fractional derivatives, I and I are the Riemann-Liouville fractional integrals, and 0 < γ < 1 < β < 2 < α < 3, ν,ω > 0, 0 < η, ξ < 1, k ∈R, f ∈ C([0, 1]×R×R,R), g ∈ C([0, 1]×R,R). The p-Laplacian operator is defined as φp(t) = |t|p–2t, p > 1, and (φp) = φq, 1 p + 1 q = 1. The study of boundary value problems in the setting of fractional cal...