In this paper, we firstly obtain the existence of the monotone positive solutions and establish a corresponding iterative scheme for the following mixed-order four-point boundary value problem with p-Laplacian (φp(D α 0+u(t))) ′ + a(t)f(t, u(t), u′(t)) = 0, 0 < t < 1, u′(0)− βu(ξ) = 0, u′′(0) = 0, u′(1) + γu(η) = 0. Unlike many other fractional boundary value problem with p-Laplacian, the nonli...

The need to build a link between the structure of a complex network and the dynamical properties of the corresponding complex system (comprised of multiple low dimensional systems) has recently become apparent. Several attempts to tackle this problem have been made and all focus on either the controllability or synchronisability of the network — usually analyzed by way of the master stability f...

We study the existence of non-zero positive solutions a class systems differential equations driven by fractional powers Laplacian. Our approach is based on notion fixed point index, and allows us to deal with non-local functional weights boundary conditions. present two examples shed light type functionals growth conditions that can be considered our approach.

In this paper, we study φ-Laplacian problems for differential inclusions with Dirichlet boundary conditions. We prove the existence of solutions under both convexity and nonconvexity conditions on the multivalued right-hand side. The nonlinearity satisfies either a Nagumotype growth condition or an integrably boundedness one. The proofs rely on the Bonhnenblust-Karlin fixed point theorem and th...

In this article, we study a class of fractional coupled systems with Riemann-Stieltjes integral boundary conditions and generalized p-Laplacian which involves two different parameters. Based on the Guo-Krasnosel’skii fixed point theorem, some new results on the existence and nonexistence of positive solutions for the fractional system are received, the impact of the two different parameters on ...

In this paper, we establish the existence of three positive solutions to the following p-Laplacian functional dynamic equation on time scales, [Φp(u ∆(t))]∇ + a(t)f(u(t), u(μ(t))) = 0, t ∈ (0, T )T, u0(t) = φ(t), t ∈ [−r, 0]T, u(0)−B0(u(η)) = 0, u(T ) = 0, . using the fixed-point theorem due to Avery and Peterson [8]. An example is given to illustrate the main result.

In this paper, we establish existence of positive solutions of the nonlinear problems of one dimensional p-Laplacian with nonlinear parameter φp(u ′(t))′ + a(t)f(λ, u) = 0, t ∈ (0, 1), u(0) = u(1) = 0. where a : Ω→ R is continuous and may change sign, λ > 0 is a parameter, f(λ, 0) > 0 for all λ > 0. By applying Leray-Schauder fixed point theorem we obtain the existence of positive solutions.

In the present paper, we deal with two different existence results of solutions for a nonlocal elliptic Dirichlet boundary value problem involving p(x)-Laplacian. The first one is based on the Brouwer fixed point theorem and the Galerkin method which gives a priori estimate of a nontrivial weak soltion. The second one is based on the variational methods. By using Mountain-Pass theorem, we obtai...

Weak solutions for nonlinear wave equations involving the p(x)Laplacian, for p : Ω → (1,∞) are constructed as appropriate limits of solutions of an implicit finite element discretization of the problem. A simple fixed-point scheme with appropriate stopping criteria is proposed to conclude convergence for all discretization, regularization, perturbation, and stopping parameters tending to zero. ...

By using the fixed point theory for completely continuous operator, this paper investigates the existence of positive solutions for a class of fourth-order impulsive boundary value problems with integral boundary conditions and one-dimensional p-Laplacian. Moreover, we offer some interesting discussion of the associated boundary value problems. Upper and lower bounds for these positive solution...