p-Laplacian
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Investigation of the p-Laplacian nonperiodic nonlinear boundary value problem via generalized Caputo fractional derivatives Open
A newly proposed p -Laplacian nonperiodic boundary value problem is studied in this research paper in the form of generalized Caputo fractional derivatives. The existence and uniqueness of solutions are fully investigated for this problem …
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Stability of variational eigenvalues for the fractional $p-$Laplacian Open
By virtue of Γ-convergence arguments, we investigate the stability of variational eigenvalues associated with a given topological index for the fractional p-Laplacian operator, in the singular limit as the nonlocal operator converges to th…
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Positive solutions for a system of nonlinear fractional nonlocal boundary value problems with parameters and p-Laplacian operator Open
In this paper, we investigate the existence of positive solutions for a system of nonlinear fractional differential equations nonlocal boundary value problems with parameters and p-Laplacian operator. Under different combinations of superl…
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Positive solutions to boundary value problems of p-Laplacian with fractional derivative Open
In this article, we consider the following boundary value problem of nonlinear fractional differential equation with p-Laplacian operator: $$\begin{aligned}& D^{\alpha}\bigl(\phi_{p}\bigl(D^{\alpha}u(t) \bigr)\bigr)= f\bigl(t, u(t)\bigr), …
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Infinitely many solutions for the stationary Kirchhoff problems involving the fractional<i>p</i>-Laplacian Open
The aim of this paper is to establish the multiplicity of weak solutions for a Kirchhoff-type problem driven by a fractional p-Laplacian operator with homogeneous Dirichlet boundary conditions.
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Multiplicity and concentration results for some nonlinear Schrödinger equations with the fractional <i>p</i>-Laplacian Open
We consider a class of parametric Schrödinger equations driven by the fractional p-Laplacian operator and involving continuous positive potentials and nonlinearities with subcritical or critical growth. Using variational methods and Ljuste…
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EXISTENCE THEOREMS AND HYERS-ULAM STABILITY FOR A CLASS OF HYBRID FRACTIONAL DIFFERENTIAL EQUATIONS WITH P -LAPLACIAN OPERATOR Open
In this paper, we prove necessary conditions for existence and uniqueness of solution (EUS) as well Hyers-Ulam stability for a class of hybrid fractional differential equations (HFDEs) with p-Laplacian operator. For these aims, we take hel…
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Symmetry results for critical anisotropic p-Laplacian equations in convex cones Open
Given n≥ 2 and 1 < p< n, we consider the critical p-Laplacian equation Δpu+up∗-1=0, which corresponds to critical points of the Sobolev inequality. Exploiting the moving planes method, it has been recently shown that positive solutio…
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Existence theorems and Hyers-Ulam stability for a coupled system of fractional differential equations with p-Laplacian operator Open
In this paper, we study the existence and uniqueness of solution (EUS) as well as Hyers-Ulam stability for a coupled system of FDEs in Caputo’s sense with nonlinear p-Laplacian operator. For this purpose, the suggested coupled system is tr…
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Positive solutions for nonlinear singular elliptic equations of p-Laplacian type with dependence on the gradient Open
In this paper, we study a nonlinear Dirichlet problem of p-Laplacian type with combined effects of nonlinear singular and convection terms. An existence theorem for positive solutions is established as well as the compactness of solution s…
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Existence of solutions for hybrid modified ABC-fractional differential equations with p-Laplacian operator and an application to a waterborne disease model Open
In this article, we investigate some necessary and sufficient conditions required for the existence of solutions for modified ABC-fractional differential equations (mAB-FDEs) with p-Laplacian operator. We also study the uniqueness and Hyer…
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Existence criterion for the solutions of fractional order p-Laplacian boundary value problems Open
\n The existence criterion has been extensively studied for different classes in fractional differential equations (FDEs) through different mathematical methods. The class of fractional order boundary value problems (FOBVPs) with p-Laplaci…
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Iterative unique positive solutions for singular p-Laplacian fractional differential equation system with several parameters Open
By using the method of reducing the order of a derivative, the higher-order fractional differential equation is transformed into the lower-order fractional differential equation and combined with the mixed monotone operator, a unique posit…
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A comparative study on nonlocal diffusion operators related to the fractional Laplacian Open
In this paper, we study four nonlocal diffusion operators, including the\nfractional Laplacian, spectral fractional Laplacian, regional fractional\nLaplacian, and peridynamic operator. These operators represent the\ninfinitesimal generator…
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Positive solutions for the Robin <i>p</i>-Laplacian problem with competing nonlinearities Open
We consider a parametric nonlinear elliptic equation driven by the Robin p -Laplacian. The reaction term is a Carathéodory function which exhibits competing nonlinearities (concave and convex terms). We prove two bifurcation-type results d…
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Positive solution for a fractional singular boundary value problem with p-Laplacian operator Open
In this paper, we consider a fractional singular three-point boundary value problem with p-Laplacian operator. The nonlinearity f(t,u) $f(t,u)$ may be singular at t=0,1 $t = 0,1$ and u=0 $u = 0$. Some properties of the associated Green fun…
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Fractional elliptic equations with critical exponential nonlinearity Open
We study the existence of positive solutions for fractional elliptic equations of the type (-Δ) 1/2 u = h ( u ), u > 0 in (-1,1), u = 0 in ℝ∖(-1,1) where h is a real valued function that behaves like e u 2 as u → ∞ . Here (-Δ) 1/2 is the f…
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On the Evolutionary Fractional<i>p</i>-Laplacian Open
In this work, existence results on nonlinear first order as well as doubly nonlinear second-order evolution equations involving the fractional |$p$|-Laplacian are presented. The proofs do not exploit any monotonicity assumption but rely on…
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Existence of solutions for a class of p(x)-laplacian equations involving a concave-convex nonlinearity with critical growth in R^{N} Open
We prove the existence of solutions for a class of quasilinear problems involving variable exponents and\nwith nonlinearity having critical growth. The main tool used is the variational method, more precisely, Ekeland's Variational Princip…
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Saddle point solutions for non-local elliptic operators Open
The paper deals with equations driven by a non-local integrodifferential operator Lk with homogeneous Dirichlet boundary conditions. These equations have a variational structure and we find a solution for them using the Saddle Point Theore…
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Oscillation Theorems for Advanced Differential Equations with p-Laplacian Like Operators Open
The main objective of this paper is to establish new oscillation results of solutions to a class of even-order advanced differential equations with a p-Laplacian like operator. The key idea of our approach is to use the Riccati transformat…
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Global Hölder regularity for the fractional $p$-Laplacian Open
By virtue of barrier arguments we prove C^\alpha -regularity up to the boundary for the weak solutions of a non-local, non-linear problem driven by the fractional p -Laplacian operator. The equation is boundedly inhomogeneous and the bound…
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Positive Solutions for a Class of p-Laplacian Hadamard Fractional-Order Three-Point Boundary Value Problems Open
In this paper, using the Avery–Henderson fixed point theorem and the monotone iterative technique, we investigate the existence of positive solutions for a class of p-Laplacian Hadamard fractional-order three-point boundary value problems.
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On a nonlinear Hadamard type fractional differential equation with p-Laplacian operator and strip condition Open
Under certain nonlinear growth conditions of the nonlinearity, we investigate the existence of solutions for a nonlinear Hadamard type fractional differential equation with strip condition and p-Laplacian operator.At the end, two examples …
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Improved Approach for Studying Oscillatory Properties of Fourth-Order Advanced Differential Equations with p-Laplacian Like Operator Open
This paper aims to study the oscillatory properties of fourth-order advanced differential equations with p-Laplacian like operator. By using the technique of Riccati transformation and the theory of comparison with first-order delay equati…
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Positive solutions to fractional boundary-value problems with p-Laplacian on time scales Open
In this article, we consider the following boundary-value problem of nonlinear fractional differential equation with p-Laplacian operator: Dα(ϕp(Dαu(t)))=f(t,u(t)),t∈[0,1]T,u(0)=u(σ(1))=Dαu(0)=Dαu(σ(1))=0, $$\begin{aligned}& D^{\alpha }\bi…
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Operator error estimates for homogenization of fourth order elliptic equations Open
Homogenization of elliptic divergence-type fourth-order operators with $\varepsilon$-periodic coefficients is studied. Here $\varepsilon$ is a small parameter. Approximations for the resolvent are obtained in the $(L^2\to L^2)$- and $(L^2\…
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Solutions of nonlinear problems involving <i>p</i> ( <i>x</i> )-Laplacian operator Open
In the present paper, by using variational principle, we obtain the existence and multiplicity of solutions of a nonlocal problem involving p ( x )-Laplacian. The problem is settled in the variable exponent Sobolev space W 0 1, p ( x ) (Ω)…
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Study on the stability and its simulation algorithm of a nonlinear impulsive ABC-fractional coupled system with a Laplacian operator via F-contractive mapping Open
In this paper, we study the solvability and generalized Ulam–Hyers (UH) stability of a nonlinear Atangana–Baleanu–Caputo (ABC) fractional coupled system with a Laplacian operator and impulses. First, this system becomes a nonimpulsive syst…
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Existence and uniqueness of solutions for fractional boundary value problems with p-Laplacian operator Open
In this paper, we investigate the existence and uniqueness of solutions for a fractional boundary value problem involving the p-Laplacian operator. Our analysis relies on some properties of the Green function and the Guo-Krasnoselskii fixe…