Doubtnut is No.1 Study App and Learning App with Instant Video Solutions for NCERT Class 6, Class 7, Class 8, Class 9, Class 10, Class 11 and Class 12, IIT JEE prep, NEET preparation and CBSE, UP Board, Bihar Board, Rajasthan Board, MP Board, Telangana Board etc NCERT solutions for...
Doubtnut is No.1 Study App and Learning App with Instant Video Solutions for NCERT Class 6, Class 7, Class 8, Class 9, Class 10, Class 11 and Class 12, IIT JEE prep, NEET preparation and CBSE, UP Board, Bihar Board, Rajasthan Board, MP Board, Telangana Board etc NCERT solutions for...
is the so-called Coulomb energy of the wave. In equation (1.1), we setq:=2(4+α)2+α, which is a critical end point of the admission interval ofrin the Coulomb–Sobolev inequality ∫RN|ϕ|rdx≤C‖∇ϕ‖2r(N+α)−4N4+α−N[L(ϕ)]2N−r(N−2)2(4+α−N) (1....
Mathematical work on nonlinear Choquard equations like the above has been investigated in recent years, and the existence and multiplicity results for such type equations have been considered in many papers under some different assumptions on the potential and nonlinearity by using various variational arg...
Moreover, we prove the nonexistence of the PST for several other classes of integral circulant graphs whose order is divisible by 4. These classes cover the class of integral circulant graphs where the divisor set contains exactly two elements. These results partially answer the main question of ...
Main result and discussion Theorem 9 Steady-State Operation Consider the power system dynamics (5) , a solution (is,v)∈Pω0 to the nodal current balance equations, and iT=ZT−1E⊤v. The power system operates in steady state if and only if: Theorem 9 combines necessary and sufficient...
At first I will give complete definitions, state and prove simple lemmas, etc., in order to establish common language. As time progresses I expect that things will become a little more high-level, less self-contained, and more technical. Depending on your background and interests, you may ...
We divide our paper into four sections. In Sect.2, we give some notations and preliminary results. In Sects.3and4, we prove Theorems2.1and2.2. The main difficulties that arise in treating this class of nonhomogeneous Schrödinger equations (2.2) are the following: (i) the lack of compactn...
Doubtnut is No.1 Study App and Learning App with Instant Video Solutions for NCERT Class 6, Class 7, Class 8, Class 9, Class 10, Class 11 and Class 12, IIT JEE prep, NEET preparation and CBSE, UP Board, Bihar Board, Rajasthan Board, MP Board, Telangana Board etc NCERT solutions for...
Doubtnut is No.1 Study App and Learning App with Instant Video Solutions for NCERT Class 6, Class 7, Class 8, Class 9, Class 10, Class 11 and Class 12, IIT JEE prep, NEET preparation and CBSE, UP Board, Bihar Board, Rajasthan Board, MP Board, Telangana Board etc NCERT solutions for...