A variational approach for boundary value problems for impulsive fractional differential equations

• Published in: Fractional calculus & applied analysis Vol. 21; no. 6; pp. 1565 - 1584
• Main Authors: Afrouzi, Ghasem A., Hadjian, Armin
• Format: Journal Article
• Language: English
• Published: Warsaw Versita 01.12.2018; De Gruyter; Nature Publishing Group
• Subjects: 26A33; 58E05; 58E30; Abstract Harmonic Analysis; Analysis; Boundary value problems; Critical point; Differential equations; fractional differential equations; Functional Analysis; impulsive conditions; infinitely many solutions; Integral Transforms; Mathematical analysis; Mathematics; Nonlinearity; Operational Calculus; Primary 34A08; Research Paper; Secondary 34B37; weak and classical solutions; infinitely many solutions; Primary 34A08; 58E05; 26A33; impulsive conditions; Secondary 34B37; 58E30; fractional differential equations; weak and classical solutions
• ISSN: 1311-0454; 1314-2224
• DOI: 10.1515/fca-2018-0082

By using an abstract critical point result for differentiable and parametric functionals due to B. Ricceri, we establish the existence of infinitely many classical solutions for fractional differential equations subject to boundary value conditions and impulses. More precisely, we determine some intervals of parameters such that the treated problems admit either an unbounded sequence of solutions, provided that the nonlinearity has a suitable oscillatory behaviour at infinity, or a pairwise distinct sequence of solutions that strongly converges to zero if a similar behaviour occurs at zero. No symmetric condition on the nonlinear term is assumed. Two examples are then given.