Existence and multiplicity result for a fractional p-Laplacian equation\n with combined fractional derivatives

2017/03/07 by Torres, César, Nemat Nyamoradi, Nyamoradi, Nemat +1
Computer Science · Mathematics · #26A33 #35A15 #35B38 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1703.02450

openalex publication_date 2017/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to obtain the existence of solutions for the\nfollowing fractional p-Laplacian Dirichlet problem with mixed derivatives\n namp;_tD_T
^alpha
left(|₀D_t
^alphau(t)|^p-2₀D_t
^alphau(t)
right)\n= f(t, u(t)),
;t
in [0,T],

amp;u(0) = u(T) = 0, where 0 <\n\α <1, 1<p<\∞ and f:[0,T]\× \ℝ \→ \ℝ is a\ncontinuous function. We obtain the existence of nontrivial solutions by using\nthe direct method in variational methods and the genus in the critical point\ntheory. Furthermore, if 0< \α < \(1)/(p) we obtain an almost every\nwhere classical solution.\n

Citations

• Fractional dynamics of populations
• Existence and symmetric result for Liouville-Weyl fractional nonlinear Schrödinger equation

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