Basis Properties of Fu?ík Eigenfunctions

BASIS PROPERTIES OF EIGENFUNCTIONS OF THE p-LAPLACIAN

For p 12 11 , the eigenfunctions of the non-linear eigenvalue problem for the p-Laplacian on the interval (0, 1) are shown to form a Riesz basis of L2(0, 1) and a Schauder basis of Lq(0, 1) whenever 1 < q < ∞.

Properties of Sturm-Liouville Eigenfunctions and Eigenvalues

control of the optical properties of nanoparticles by laser fields

در این پایان نامه، درهمتنیدگی بین یک سیستم نقطه کوانتومی دوگانه(مولکول نقطه کوانتومی) و میدان مورد مطالعه قرار گرفته است. از آنتروپی ون نیومن به عنوان ابزاری برای بررسی درهمتنیدگی بین اتم و میدان استفاده شده و تاثیر پارامترهای مختلف، نظیر تونل زنی(که توسط تغییر ولتاژ ایجاد می شود)، شدت میدان و نسبت دو گسیل خودبخودی بر رفتار درجه درهمتنیدگی سیستم بررسی شده اشت.با تغییر هر یک از این پارامترها، در...

On the Existence, Uniqueness, and Basis Properties of Radial Eigenfunctions of a Semilinear Second-Order Elliptic Equation in a Ball

We consider the following eigenvalue problem: −Δu f u λu, u u x , x ∈ B {x ∈ R3 : |x| < 1}, u 0 p > 0, u||x| 1 0, where p is an arbitrary fixed parameter and f is an odd smooth function. First, we prove that for each integer n ≥ 0 there exists a radially symmetric eigenfunction un which possesses precisely n zeros being regarded as a function of r |x| ∈ 0, 1 . For p > 0 sufficiently small, such...

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...