NONTRIVIAL SOLUTIONS FOR BOUNDARY-VALUE PROBLEMS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS
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In this paper, we consider the existence of nontrivial solutions for the nonlinear fractional differential equation boundary-value problem (BVP)−Dα0+u(t) = λ[f(t, u(t)) + q(t)], 0 < t < 1u(0) = u(1) = 0,where λ > 0 is a parameter, 1 < α ≤ 2, Dα0+ is the standard Riemann-Liouville differentiation, f : [0, 1] × R → R is continuous, and q(t) :(0, 1) → [0,+∞) is Lebesgue integrable. We obtain serval sufficient conditions of the existence and uniqueness of nontrivial solution of BVP when λ in some interval. Our approach is based on Leray-Schauder nonlinear alternative. Particularly, we do not use the nonnegative assumption and monotonicity which was essential for the technique used in almost all existed literature on f.
Abstract
In this paper, we consider the existence of nontrivial solutions for the nonlinear fractional differential equation boundary-value problem (BVP)−Dα0+u(t) = λ[f(t, u(t)) + q(t)], 0 < t < 1u(0) = u(1) = 0,where λ > 0 is a parameter, 1 < α ≤ 2, Dα0+ is the standard Riemann-Liouville differentiation, f : [0, 1] × R → R is continuous, and q(t) :(0, 1) → [0,+∞) is Lebesgue integrable. We obtain serval sufficient conditions of the existence and uniqueness of nontrivial solution of BVP when λ in some interval. Our approach is based on Leray-Schauder nonlinear alternative. Particularly, we do not use the nonnegative assumption and monotonicity which was essential for the technique used in almost all existed literature on f.
참고문헌 (9)
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