fractional differential equationboundary value problemp-Laplacian operatornoncompactness measureIn this paper, we study the solutions for nonlinear fractional differential equations with p-Laplacian operator nonlocal boundary value problem in a Banach space. By means of the technique of the properties of ...
t∈[0,T ] is a Banach space. Then 1 Throughout this paper, we denote Br = {x ∈ CT : x < r} and we make the following assumptions: (H1) There exist constants d 0, M 0 with M (T /2)p < 1, such that for |x| > d, x, g(t, x(t)) M |x|p (3) and g(t, ...
和y为Banach空间, 为 中的一个锥.考虑算子方程Lu=Nu,其中 ndomL≠,L:doraLC —y为线性算子,Ⅳ为非线性算子. 定义2.1 若 为线性算子,满足dimKerL=codimImL<∞,且Im￡为y中的闭集,则称 为指标为 零的Fredholm算子. 定义2.2 若 为线性空间,P: ...
Sandwich pairs In this section we construct sandwich pairs applicable to our problem (1.3). Let W be a Banach space and let Σ be the class of maps σ∈ C (W × [0, 1], W ) such that, writing σt = σ (·, t), (i) σ0 = id, (ii) sup(u,t)∈W ×[0,1] σt (u...
We consider the fractional Sobolev spaceWs,p(Ω)={u∈Lp(Ω):[u]Ws,p(Ω)<∞}, which is a Banach space with respect to the norm‖u‖Ws,p(Ω):=[u]Ws,p(Ω)+‖u‖Lp(Ω). Following [12] we denote by W˜0s,p(Ω) the closure of C0∞(Ω) in the normu↦[u]Ws,p(RN...
Then (X,‖⋅‖X) is a uniformly convex (and hence reflexive) Banach space. 3 Existence of principal eigenfunctions In this section we study the eigenvalue problem (1.1). Any weak solution u≠0 of (1.1) is called an eigenfunction corresponding to an eigenvalueλ. More precisely, u is ...
Using Mawhin’s continuation theorem we obtain some existence results of periodic solutions for a type of p-Laplacian neutral Liénard equation $$\left( {\phi _p \left( {\left( {x\left( t \right) - c\left( t \right)x\left( {t - \tau } \right)} \right)^\p
In this paper, we study the existence of periodic solutions for a class of ordinary p-Laplacian systems. Our technique is based on the generalized mountain pass theorem of Rabinowitz.
Let 0<\alpha\leq1 and 1< p<\infty. The fractional derivative space E_{0}^{\alpha,p} is a reflexive and separable Banach space.Lemma 3.2(see [13, 14])Let 0<\alpha\leq1 and 1< p<\infty. For u\in E_{0}^{\alpha,p}, we have \|u\|_{L^{p}}\leq\frac{T^{\alpha}}...
Cingolani, S, Vannella, G: Marino-Prodi perturbation type results and Morse indices of minimax critical points for a class of functionals in Banach space. Ann. Mat. Pura Appl. 186, 155-183 (2007) 6. Sun, MZ: Multiplicity solutions for a class of the quasilinear elliptic equations at ...