共查询到20条相似文献,搜索用时 31 毫秒
1.
Ricardo Enguiça 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(9):2968-2979
We start by studying the existence of positive solutions for the differential equation
u″=a(x)u−g(u), 相似文献
2.
Existence of positive solution for some class of nonlinear fractional differential equations 总被引:1,自引:0,他引:1
Shuqin Zhang 《Journal of Mathematical Analysis and Applications》2003,278(1):136-148
In this paper, we investigate the multiple and infinitely solvability of positive solutions for nonlinear fractional differential equation Du(t)=tνf(u), 0<t<1, where D=t−βδDβγ−δ,δ, β>0, γ?0, 0<δ<1, ν>−β(γ+1). Our main work is to deal with limit case of f(s)/s as s→0 or s→∞ and Φ(s)/s, Ψ(s)/s as s→0 or s→∞, where Φ(s), Ψ(s) are functions connected with function f. In J. Math. Appl. 252 (2000) 804-812, we consider the existence of a positive solution for the particular case of Eq. (1.1), i.e., the Riemann-Liouville type (β=1, γ=0) nonlinear fractional differential equation, using the super-lower solutions method. Here, we devote to the existence of positive solution and multi-positive solutions for Eq. (1.1) by means of the fixed point theorems for the cone. 相似文献
3.
We are concerned with the existence of least energy solutions of nonlinear Schrödinger equations involving the fractional Laplacian for sufficiently large λ, 2 < p < \(\frac{{2N}}{{N - 2s}}\) for N ≥ 2. V (x) is a real continuous function on RN. Using variational methods we prove the existence of least energy solution u λ(x) which localizes near the potential well int V ?1(0) for λ large. Moreover, if the zero sets int V ?1(0) of V (x) include more than one isolated component, then u λ(x) will be trapped around all the isolated components. However, in Laplacian case s = 1, when the parameter λ is large, the corresponding least energy solution will be trapped around only one isolated component and become arbitrarily small in other components of int V ?1(0). This is the essential difference with the Laplacian problems since the operator (?Δ)s is nonlocal.
相似文献
$$\begin{array}{*{20}c} {( - \Delta )^s u(x) + \lambda V(x)u(x) = u(x)^{p - 1} ,} & {u(x) \geqslant 0,} & {x \in \mathbb{R}^N ,} \\ \end{array} $$
4.
Y. Guo 《Ukrainian Mathematical Journal》2011,62(9):1409-1419
We consider the existence of nontrivial solutions of the boundary-value problems for nonlinear fractional differential equations
*20c Da u(t) + l[ f( t,u(t) ) + q(t) ] = 0, 0 < t < 1, u(0) = 0, u(1) = bu(h), \begin{array}{*{20}{c}} {{{\mathbf{D}}^\alpha }u(t) + {{\lambda }}\left[ {f\left( {t,u(t)} \right) + q(t)} \right] = 0,\quad 0 < t < 1,} \\ {u(0) = 0,\quad u(1) = \beta u(\eta ),} \\ \end{array} 相似文献
5.
In this paper, we consider the following nonlinear fractional three-point boundary-value problem:
|