共查询到20条相似文献,搜索用时 46 毫秒
1.
In this paper we consider the bifurcation problem -div A(x, u)=λa(x)|u|^p-2u+f(x,u,λ) in Ω with p 〉 1.Under some proper assumptions on A(x,ξ),a(x) and f(x,u,λ),we show that the existence of an unbounded branch of positive solutions bifurcating Irom the principal eigenvalue of the problem --div A(x, u)=λa(x)|u|^p-2u. 相似文献
2.
We consider a nonoscillatory half-linear second order differential equation (*) $$ (r(t)\Phi (x'))' + c(t)\Phi (x) = 0,\Phi (x) = \left| x \right|^{p - 2} x,p > 1, $$ and suppose that we know its solution h. Using this solution we construct a function d such that the equation (**) $$ (r(t)\Phi (x'))' + [c(t) + \lambda d(t)]\Phi (x) = 0 $$ is conditionally oscillatory. Then we study oscillations of the perturbed equation (**). The obtained (non)oscillation criteria extend existing results for perturbed half-linear Euler and Euler-Weber equations. 相似文献
3.
Suppose that X is a complex Banach space with the norm ‖·‖ and n is a positive integer with dim X ⩾ n ⩾ 2. In this paper, we consider the generalized Roper-Suffridge extension operator $
\Phi _{n,\beta _2 ,\gamma _2 , \ldots ,\beta _{n + 1} ,\gamma _{n + 1} } (f)
$
\Phi _{n,\beta _2 ,\gamma _2 , \ldots ,\beta _{n + 1} ,\gamma _{n + 1} } (f)
on the domain $
\Omega _{p_1 ,p_2 , \ldots ,p_{n + 1} }
$
\Omega _{p_1 ,p_2 , \ldots ,p_{n + 1} }
defined by
$
\Phi _{n,\beta _2 ,\gamma _2 , \ldots ,\beta _{n + 1} ,\gamma _{n + 1} } (f)(x) = {*{20}c}
{\sum\limits_{j = 1}^n {\left( {\frac{{f(x_1^* (x))}}
{{x_1^* (x)}}} \right)} ^{\beta _j } (f'(x_1^* (x)))^{\gamma _j } x_1^* (x)x_j } \\
{ + \left( {\frac{{f(x_1^* (x))}}
{{x_1^* (x)}}} \right)^{\beta _{n + 1} } (f'(x_1^* (x)))^{\gamma _{n + 1} } \left( {x - \sum\limits_{j = 1}^n {x_1^* (x)x_j } } \right)} \\
$
\Phi _{n,\beta _2 ,\gamma _2 , \ldots ,\beta _{n + 1} ,\gamma _{n + 1} } (f)(x) = \begin{array}{*{20}c}
{\sum\limits_{j = 1}^n {\left( {\frac{{f(x_1^* (x))}}
{{x_1^* (x)}}} \right)} ^{\beta _j } (f'(x_1^* (x)))^{\gamma _j } x_1^* (x)x_j } \\
{ + \left( {\frac{{f(x_1^* (x))}}
{{x_1^* (x)}}} \right)^{\beta _{n + 1} } (f'(x_1^* (x)))^{\gamma _{n + 1} } \left( {x - \sum\limits_{j = 1}^n {x_1^* (x)x_j } } \right)} \\
\end{array}
相似文献
4.
Regularly varying solutions of half-linear functional differential equations with retarded arguments
T. Tanigawa 《Acta Mathematica Hungarica》2008,120(1-2):53-78
We consider half-linear retarded functional differential equations of the form $$ (|x'(t)|^\alpha \operatorname{sgn} x'(t))' = q(t)|x(g(t))|^\alpha \operatorname{sgn} x(g(t)), \alpha > 0, g(t) < t $$ and obtain a necessary and sufficient condition to possess a slowly varying solution and a regularly varying solution of index 1 at the same time. 相似文献
5.
H. G. Ghazaryan V. N. Margaryan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2010,45(4):239-249
It is proved that if P(D) is a regular, almost hypoelliptic operator and
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