2018
DOI: 10.1186/s13661-018-1012-0
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Infinitely many solutions for impulsive fractional boundary value problem with p-Laplacian

Abstract: This paper deals with the existence of infinitely many solutions for a class of impulsive fractional boundary value problems with p-Laplacian. Based on a variant fountain theorem, the existence of infinitely many nontrivial high or small energy solutions is obtained. In addition, two examples are worked out to illustrate the effectiveness of the main results. MSC: 26A33; 34B15

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Cited by 43 publications
(23 citation statements)
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“…Fractional calculus is an excellent tool for the description of the process of mathematical analysis in various areas of finance, physical systems, control systems and mechanics, and so forth [1][2][3][4][5]. Many methods are used to study various fractional differential equations, such as fixed point index theory [6], iterative method [7][8][9], theory of linear operator [10,11] sequential techniques, and regularization [12], fixed point theorems [13][14][15][16][17], the Mawhin continuation theorem for resonance [18][19][20][21][22], the variational method [23]. The definition of the fractional order derivative used in the aforementioned results is either the Caputo or the Riemann-Liouville fractional order derivative.…”
Section: Introductionmentioning
confidence: 99%
“…Fractional calculus is an excellent tool for the description of the process of mathematical analysis in various areas of finance, physical systems, control systems and mechanics, and so forth [1][2][3][4][5]. Many methods are used to study various fractional differential equations, such as fixed point index theory [6], iterative method [7][8][9], theory of linear operator [10,11] sequential techniques, and regularization [12], fixed point theorems [13][14][15][16][17], the Mawhin continuation theorem for resonance [18][19][20][21][22], the variational method [23]. The definition of the fractional order derivative used in the aforementioned results is either the Caputo or the Riemann-Liouville fractional order derivative.…”
Section: Introductionmentioning
confidence: 99%
“…It is well known that the above model (1.5) can be written as the following extension (see [20,23,24]):…”
Section: )mentioning
confidence: 99%
“…where C D α 1-and D become a popular research field. At present, many researchers study the existence of solutions of fractional differential equations such as the Riemann-Liouville fractional derivative problem at nonresonance [6][7][8][9][10][11][12][13][14][15][16], the Riemann-Liouville fractional derivative problem at resonance [17][18][19][20][21][22][23], the Caputo fractional boundary value problem [6,24,25], the Hadamard fractional boundary value problem [26][27][28], conformable fractional boundary value problems [29][30][31][32], impulsive problems [33][34][35], boundary value problems [8,[36][37][38][39][40][41][42][43], and variational structure problems [44,45].…”
Section: Introductionmentioning
confidence: 99%