本文選題：半線性發(fā)展方程 + 積分-微分方程　； 參考：《曲阜師范大學(xué)》2017年碩士論文

【摘要】：近年來,分?jǐn)?shù)階微分方程被廣泛應(yīng)用于光學(xué)和熱學(xué)系統(tǒng),電磁學(xué),控制和機(jī)器人等諸多領(lǐng)域,已經(jīng)引起國內(nèi)外數(shù)學(xué)及自然科學(xué)界的高度重視.非線性分?jǐn)?shù)階微分方程解的存在性研究是國際熱點研究方向之一.非線性分?jǐn)?shù)階微分方程是數(shù)學(xué)中的一個既有深刻理論意義又有廣泛應(yīng)用價值的研究方向.本文主要利用非線性泛函分析理論和方法研究分?jǐn)?shù)階脈沖半線性發(fā)展方程和一類p-Laplacian奇異邊值問題解的存在性和解的性質(zhì).本文共分為以下三章:第一章,我們運(yùn)用C_0半群和Banach壓縮映射原理研究Bauach空間(E，‖·‖)上的分?jǐn)?shù)階脈沖半線性發(fā)展方程適度解的存在性其中0 q 1, 是Caputo型分?jǐn)?shù)階導(dǎo)數(shù),A是C0半群(G(t))t≥0的無窮小生成元,0 t1 t2 … tm T0, f ∈ C(J × E×E, E), Ik ∈ C(E, E) (k = 1,2, …m), u0 ∈ E.T是線性算子(Tu)(t)=∫0t k(t,s)u(s)ds,t∈J,其中 kC ∈ (-∞,+∞),D={(t,s)∈J×J:t≥s}.△u|t=tk=u(tk+) -u(tk-), 其中u(tk-)和u(tk+)分別代表u(t)在t=tk處的左極限和右極限.第二章,我們研究Banach空間(E,‖·‖)上的混合型分?jǐn)?shù)階脈沖半線性積分-微分方程非局部問題適度解的存在性其中0 q 1,是Caputo型分?jǐn)?shù)階導(dǎo)數(shù),A是C0半群(G(t))t0的無窮小生成元,0 tx t2 … tm T0, f ∈ C(J × E × E × E, E), Ik ∈ C(E, E) (kk = 1, 2, …m),g∈ (J,E], E),u0 ∈ E. T 和 S 是線性算子(Tu)(t)=∫0t k(t,s)u(s)ds,(Su)(t)=∫0T0h(t, s)u(s)ds, t∈J,其中 k∈ ∈C(D,(-∞,+∞)),D= {{(t,s∈ J × J : t ≥s }, ∈C(J ×Jt, (-∞,+∞O).△u|t=tk=u(tk+)-u(tk),其中u(tk-)和u(tk+)分別代表u(t)在t= k處的左極限和右極限.第三章,我們運(yùn)用上下解方法和不動點理論研究一類分?jǐn)?shù)階p-Laplacian奇異邊值問題解的存在性其中 α ∈ (1,2], β∈(3,4],D_(0+)~α,D_(0+)~β是 Riemann-Liouville型分?jǐn)?shù)階導(dǎo)數(shù),f ∈C((0,1)×(0, +∞),[0, +∞)),f(t,u)不僅允許在t=0和/或t = 1奇異,而且允許在u = 0處奇異,Φ_p(s) = |s|p-2s, p1, Φ_p~(-1)=Φ_q,1/p + 1/q = 1, η ∈ (0,1), b ∈ (0,η(1-α/p-1)).
[Abstract]:In recent years, fractional differential equations have been widely used in many fields such as optical and thermal systems, electromagnetics, control and robots, which have aroused great attention in the field of mathematics and natural sciences at home and abroad. The existence of solutions of nonlinear fractional differential equations is one of the international hot research directions. The number of nonlinear fractional differential equations is the number of the nonlinear fractional differential equations In this paper, we mainly use the theory and method of nonlinear functional analysis to study the existence and conciliatory properties of the fractional pulse semilinear development equation and the solution of a class of p-Laplacian singular boundary value problems. This paper is divided into the following three chapters: Chapter 1, we use C_0 The principle of semigroups and Banach compression mapping studies the existence of the moderate solution of the fractional pulse semilinear development equation in the Bauach space (E), which is 0 Q 1, Caputo type fractional derivative, A is the infinitesimal generator of C0 Semigroups (G (T)) t > 0, 0 T1 T2... TM T0, f C (J x E * E, E), Ik C C (E, E) (= = =,... M), U0 E.T is a linear operator (T) = 0t K (T, s) U (s) ds. The existence of a moderate solution for the nonlocal problem of a partial differential equation is 0 Q 1, a Caputo type fractional derivative, and A is the infinitesimal fraction of the C0 semigroup (G (T)) T0, and 0 TX T2... TM T0, f f C (J x E * E * E, E), Ik C C (E), (= = 1, 2,... And G sum and sum sum and sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sums sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum sum the left and right poles are represented respectively In the third chapter, we use the upper and lower solutions and the fixed point theory to study the existence of the solution of a class of fractional p-Laplacian singular boundary value problems, in which 1,2], 3,4], D_ (0+) ~ (0+), D_ (0+) ~ beta are Riemann-Liouville type fractional derivatives, f C ((0,1) * (0, + infinity), [0, + infinity). It is allowed to be singular at u = 0, _p (s) = |s|p-2s, P1, _p~ (-1) = _q, 1/p + 1/q = 1, ETA (0,1), 1/q (0, 1/p).
【學(xué)位授予單位】：曲阜師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175.8

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 徐家發(fā);董衛(wèi);;分?jǐn)?shù)階p-Laplacian邊值問題正解的存在唯一性[J];數(shù)學(xué)學(xué)報(中文版);2016年03期

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