Nonnegative solution of a class of double phase problems with logarithmic nonlinearity

Abstract

This manuscript proves the existence of a nonnegative, nontrivial solution to a class of double-phase problems involving potential functions and logarithmic nonlinearity in the setting of Sobolev space on complete manifolds. Some applications are also being investigated. The arguments are based on the Nehari manifold and some variational techniques.

Existence Results in Weighted Sobolev Space for Quasilinear Degenerate P(z)−elliptic Problems With a Hardy Potential

“…The weighted Sobolev spaces W k,p (Ω) appear in general as solution spaces for parabolic and elliptic partial differential equations. For degenerate partial differential equations, it quite natural to try to find solutions in weighted Sobolev spaces (see [5,11,16,18,20,24] for more details).…”

Algorithms for Approximating Solutions of Split Variational Inclusion and Fixed-Point Problems

“…A special case of (1) is the split fixed point problem of finding a point q ∈ H 1 , such that q ∈ Fix(T) and Aq ∈ Fix(S), (3) which generalizes the convex feasibility problem and the two-sets split feasibility problem arising in the intensity-modulated radiation therapy [1].…”

“…There are various ways to solve the split problems, see [2][3][4][5][6][7][8][9][10][11][12][13]. To solve (3), a remarkable channel brought up by Censor and Segal [14] is of the manner:…”