NEHARI MANIFOLD AND MULTIPLICITY RESULTS FOR A CLASS OF FRACTIONAL BOUNDARY VALUE PROBLEMS WITH p-LAPLACIAN

被引：12

作者：

Ghanmi, Abdeljabbar ^{[1
,2
]}

Zhang, Ziheng ^{[3
]}

机构：

[1] Univ Jeddah, Dept Math, Fac Sci & Arts Khulais, Jeddah, Saudi Arabia

[2] Univ Tunis El Manar, Fac Sci Tunis, Tunis, Tunisia

[3] Tianjin Polytech Univ, Sch Math Sci, Tianjin 300387, Peoples R China

来源：

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY | 2019年 / 56卷 / 05期

关键词：

nonlinear fractional differential equations; boundary value problem; existence of solutions; Nehari manifold; POSITIVE SOLUTIONS;

D O I：

10.4134/BKMS.b181172

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this work, we investigate the following fractional boundary value problems {D-t(T)alpha (vertical bar D-0(t)alpha(u(t))vertical bar(p-2)(0)D(t)(alpha)u(t)) = del W (t, u(t)) + lambda g(t)vertical bar u(t)vertical bar(q-2)u(t), t is an element of (0, T), u(0) = u(T) = 0, where del W(t,u) is the gradient of W(t, u) at u and W is an element of C([0, T] x R-n, R ) is homogeneous of degree r, lambda is a positive parameter, g is an element of C([0, T]), 1 < r < p < q and 1/p < alpha < 1. Using the Fibering map and Nehari manifold, for some positive constant lambda(0) such that 0 < lambda < lambda(0), we prove the existence of at least two non-trivial solutions.

引用

页码：1297 / 1314

页数：18

共 33 条

[1]

Agarwal RP, 2009, GEORGIAN MATH J, V16, P401

[2]

Agrawal OP, 2004, Fractional derivatives and their applications: Nonlinear dynamics

[3] Analysis of a fractional SEIR model with treatment [J].