The main theme of this paper is to investigate a generalized quaternionic sequence with dual-generalized complex (DEC) Leonardo numbers via doubling depending on 3-parameters, lambda i is an element of{1,2,3}, using Cayley-Dickson doubling procedure. Firstly, we briefly describe the DEC Fibonacci, DEC Lucas and DEC Leonardo sequences via doubling. After defining the 3-parameter generalized quaternionic (3PGQic) sequence with DEC Leonardo numbers via doubling, we give the Binet's formula, the generating function, Catalan's, Cassini's and d'Ocagne's identities for this sequence. Finally, we discuss the special cases in which well-known quaternionic sequences with DEC Leonardo numbers are obtained.
We prove the existence of a renormalized solution to the problem of the nonlinear degenerate parabolic equation partial derivative u partial derivative t N X i=1 partial derivative partial derivative xi CXN ) omega i (x) aij(t, x, u) partial derivative u = f, partial derivative xj j=1 where the matrix A(t, x, s) = (aij(t, x, s))1i,jN is not controlled with respect to u and f is an element of L1(Q).
