A global implicit function theorem is given.doi:10.1016/0096-3003(95)00246-4J.M. SorianoApplied Mathematics & ComputationSoriano J M. On the existence of zero points[J].Appl Math Comput, 1996,79:99- 104.Soriano J M. On the existence of zero points. Appl Math Comput, 1996, 79: 99-...
We present a simple condition which can be used to verify that under some conditions, set-valued operators have zero points. Furthermore, we derive the surjectivity result and the Kakutani fixed point theorem by using this condition.doi:10.1007/s11228-006-0030-8Shin-ya Matsushita...
The theorem of Landesman and Lazer for nonlinear Dirichlet problems has been since repeatedly extended by the alternative method by Williams and Necas. This chapter presents an abstract problem, at resonance, of the form Ex = Nx, x ∈ S, where N : S → S is a nonlinear continuous ...
Theorem 2.17. A function is absolutely continuous on if and only if is -differentiable -almost everywhere on , and (2.16) We also recall the Banach Lemma. Lemma 2.18. Let be a Banach space and an absolutely continuous function, then the measure of the set and is zero. Using the previou...
Let { V=R^3 } and { S = \{e_1,e_2,e_3\} }.prove that S is a basis of V. What is the difference between a theorem and a proof? Prove that (\sec x + \tan x)^2 = \dfrac{1 + \sin x}{1 + \cos x}. Prove that \| u + v \|^2 - \| u - v\|^2 = 4 ...
Bai, C: Existence of three solutions for a nonlinear fractional boundary value problem via a critical points theorem. Abstr. Appl. Anal. 2012, Article ID 963105 (2012) Article Google Scholar Bai, C: Existence of solutions for a nonlinear fractional boundary value problem via a local minimum...
(There are no values of x and y that give us division by zero or an even root of a negative number, for example.) The conditions of the theorem are satisfied, and so any IVP of the form described previously has a unique solution. In Section 2.2 we showed how to find a solution of...
Theorem 1.3 Let q ∈ Cη(Ω) ∩ C2(Ωδ) for some δ > 0 be a nonnegative function with q > 0 on ∂Ω. Then there exists a unique solution to (1.1). Note that q(x) may vanish in some interior region of Ω and we still get existence and uniqueness of solutions to ...
We present here two new criteria for existence of a tame Harrison map of two formally real algebraic function fields over a fixed real closed field of constants. The first criterion (c.f. Theorem 2.5) shows that a square class group isomorphism is a tame
5) zero points 零点6) zero-point 零点 1. The existence theorem of zero-point for one class of second order nonlinear differential equation; 一类二阶非线性微分方程解的零点存在定理 2. An unchanged zero-point is a main problem in the measurement process of dynamic angle measurement. 针对所研制...