Fractional p-Laplacian Equation Research Articles

Random attractors of fractional p-Laplacian equation driven by colored noise on $${\mathbb {R}}^n$$

Random attractors of fractional p-Laplacian equation driven by colored noise on $${\mathbb {R}}^n$$

Homoclinic solutions for discrete fractional p-Laplacian equation via the Nehari manifold method

Homoclinic solutions for discrete fractional p-Laplacian equation via the Nehari manifold method

Stability of random attractors for non-autonomous fractional stochastic p-Laplacian equations driven by nonlinear colored noise

Stability of random attractors for non-autonomous fractional stochastic p-Laplacian equations driven by nonlinear colored noise

Multiple Solutions to the Fractional p-Laplacian Equations of Schrödinger–Hardy-Type Involving Concave–Convex Nonlinearities

This paper is concerned with nonlocal fractional p-Laplacian Schrödinger–Hardy-type equations involving concave–convex nonlinearities. The first aim is to demonstrate the L∞-bound for any possible weak solution to our problem. As far as we know, the global a priori bound for weak solutions to nonlinear elliptic problems involving a singular nonlinear term such as Hardy potentials has not been studied extensively. To overcome this, we utilize a truncated energy technique and the De Giorgi iteration method. As its application, we demonstrate that the problem above has at least two distinct nontrivial solutions by exploiting a variant of Ekeland’s variational principle and the classical mountain pass theorem as the key tools. Furthermore, we prove the existence of a sequence of infinitely many weak solutions that converges to zero in the L∞-norm. To derive this result, we employ the modified functional method and the dual fountain theorem.

Existence for doubly nonlinear fractional p-Laplacian equations

Existence for doubly nonlinear fractional p-Laplacian equations

Bifurcation analysis of fractional Kirchhoff problems with singular exponential nonlinearity

This paper deals with the bifurcation results of (weak) solutions for the Kirchhoff fractional p-Laplacian equation { M ( x , [ u ] s , p p ) ( − Δ ) p s u = f ( λ , x , u ) in Ω , u = 0 in R N ∖ Ω , where ( − Δ ) p s denotes the fractional operator, with sp = N, and the nonlinearity f exhibits the singular exponential growth at infinity. Moreover, the existence of unbounded components of (weak) solutions emanating from the trivial solution, is treated via the fix point result and the global bifurcation theorem due to Rabinowitz. Finally, the main feature of this paper consists of the existence of positive solutions to the above equation for λ small enough.

Existence of non-trivial solutions to a class of fractional p-Laplacian equations of Schrödinger-type with a combined nonlinearity

Existence of non-trivial solutions to a class of fractional p-Laplacian equations of Schrödinger-type with a combined nonlinearity

Monotonicity of entire solutions to reaction-diffusion equations involving fractional p-Laplacian

Abstract We obtain the one-dimensional symmetry and monotonicity of the entire positive solutions to some reaction-diffusion equations involving fractional p-Laplacian by virtue of the sliding method. More precisely, we consider the following problem { ∂ ⁡ u ∂ ⁡ t ⁢ ( x , t ) + ( - Δ ) p s ⁢ u ⁢ ( x , t ) = f ⁢ ( t , u ⁢ ( x , t ) ) , ( x , t ) ∈ Ω × ℝ , u ⁢ ( x , t ) > 0 , ( x , t ) ∈ Ω × ℝ , u ⁢ ( x , t ) = 0 , ( x , t ) ∈ Ω c × ℝ , \left\{\begin{aligned} \displaystyle{}\frac{\partial u}{\partial t}(x,t)+(-% \Delta)_{p}^{s}u(x,t)&\displaystyle=f(t,u(x,t)),&\hskip 10.0pt(x,t)&% \displaystyle\in\Omega\times\mathbb{R},\\ \displaystyle u(x,t)&\displaystyle>0,&\hskip 10.0pt(x,t)&\displaystyle\in% \Omega\times\mathbb{R},\\ \displaystyle u(x,t)&\displaystyle=0,&\hskip 10.0pt(x,t)&\displaystyle\in% \Omega^{c}\times\mathbb{R},\end{aligned}\right. where s ∈ ( 0 , 1 ) {s\in(0,1)} , p ≥ 2 {p\geq 2} , ( - Δ ) p s {(-\Delta)_{p}^{s}} is the fractional p-Laplacian, f ⁢ ( t , u ) {f(t,u)} is some continuous function, the domain Ω ⊂ ℝ n {\Omega\subset\mathbb{R}^{n}} is unbounded and Ω c = ℝ n ∖ Ω {\Omega^{c}=\mathbb{R}^{n}\setminus\Omega} . Firstly, we establish a maximum principle involving the parabolic p-Laplacian operator. Then, under certain conditions of f, we prove the asymptotic behavior of solutions far away from the boundary uniformly in t ∈ ℝ {t\in\mathbb{R}} . Finally, the sliding method is implemented to derive the monotonicity and uniqueness of the bounded positive entire solutions. To our best knowledge, there has not been any results on the symmetry and monotonicity properties of solutions to the parabolic fractional p-Laplacian equations before.

Initial value problems for fractional p-Laplacian equations with singularity

<abstract><p>We have studied initial value problems for Caputo fractional differential equations with singular nonlinearities involving the p-Laplacian operator. We have given a precise mathematical analysis of the equivalence of the fractional differential equations and Volterra integral equations studied in this paper. A theorem for the global existence of the solution was proven. In addition, an example was given at the end of the article as an application of the results found in this paper.</p></abstract>

Multi-peak Solutions of a Class of Fractional p-Laplacian Equations

Multi-peak Solutions of a Class of Fractional p-Laplacian Equations

The Effect of the Domain Topology on the Number of Positive Solutions for Fractional p-laplacian Equation with Critical Growth

The Effect of the Domain Topology on the Number of Positive Solutions for Fractional p-laplacian Equation with Critical Growth

Solvability, Approximation and Stability of Periodic Boundary Value Problem for a Nonlinear Hadamard Fractional Differential Equation with p-Laplacian

The fractional order p-Laplacian differential equation model is a powerful tool for describing turbulent problems in porous viscoelastic media. The study of such models helps to reveal the dynamic behavior of turbulence. Therefore, this article is mainly concerned with the periodic boundary value problem (BVP) for a class of nonlinear Hadamard fractional differential equation with p-Laplacian operator. By virtue of an important fixed point theorem on a complete metric space with two distances, we study the solvability and approximation of this BVP. Based on nonlinear analysis methods, we further discuss the generalized Ulam-Hyers (GUH) stability of this problem. Eventually, we supply two example and simulations to verify the correctness and availability of our main results. Compared to many previous studies, our approach enables the solution of the system to exist in metric space rather than normed space. In summary, we obtain some sufficient conditions for the existence, uniqueness, and stability of solutions in the metric space.

Entire sign-changing solutions to the fractional [formula omitted]-Laplacian equation involving critical nonlinearity

We establish the existence of multiple sign-changing solutions to the fractional p-Laplacian equation (−△)psu−|u|p∗−2u=0,inRN,by combining the minimax theory and group equivariant technique with the concentration compactness argument.

Global existence and finite time blowup for a fractional pseudo-parabolic p-Laplacian equation

Global existence and finite time blowup for a fractional pseudo-parabolic p-Laplacian equation

On a Fractional p-Laplacian Equation with Critical Fractional Sobolev Exponent

On a Fractional p-Laplacian Equation with Critical Fractional Sobolev Exponent

Fractional p-Laplacian Equations with Sandwich Pairs

The main purpose of this paper was to consider new sandwich pairs and investigate the existence of a solution for a new class of fractional differential equations with p-Laplacian via variational methods in ψ-fractional space Hpα,β;ψ(Ω). The results obtained in this paper are the first to make use of the theory of ψ-Hilfer fractional operators with p-Laplacian.

Fractional p-Laplacian differential equations with multi-point boundary conditions in Banach spaces

Fractional p-Laplacian differential equations with multi-point boundary conditions in Banach spaces

更高分数阶p-Laplacian方程的特征值问题

更高分数阶p-Laplacian方程的特征值问题

Multiplicity of Solutions for Dirichlet Problem of a Superlinear Fractional p-Laplacian Equation

This paper is dedicated to studying the following fractional p-Laplacian problem where Ω⊂ℝN (N ≥ 2) is a bounded domain with C 1,1 boundary, s∈(0,1), 2 ≤ p<N/s, (-Δ) s p is the fractional p-Laplacian and f is a (p-1)-superlinear Carathéodory reaction but does not satisfy the usual Ambrosetti-Rabinowitz condition. By using variational methods and Morse theory, we show that the equation has at least three nontrivial solutions: among one of them is positive and one is negative

Local Hölder continuity for fractional nonlocal equations with general growth

We study generalized fractional p-Laplacian equations to prove local boundedness and Hölder continuity of weak solutions to such nonlocal problems by finding a suitable fractional Sobolev-Poincaré inquality.