Existence of Positive Solutions for a Class ofpx,qx-Laplacian Elliptic Systems with

Abstract

The paper deals with the study of the existence of weak positive solutions for a new class of the system of elliptic differential equations with respect to the symmetry conditions and the right hand side which has been defined as multiplication of two separate functions by using the sub-supersolutions method (1991 Mathematics Subject Classification: 35J60, 35B30, and 35B40).

Eigenvalues of Elliptic Functional Differential Systems via a Birkhoff–Kellogg Type Theorem

“…(3) The case off i not depending on Du, withw i and h i acting on the cone of non-negative functions C(Ω, R n + ), has been studied by the author in [23]. The following example provides a system of the type (11) that cannot be handled by the theory of [14][15][16][17][18][19], due to the presence of gradient terms in the nonlinearities, and by the results in [20], due to the presence of the nonlocal BCs. It also illustrates, in contrast to previous results on Kirchhofftype systems known to the author, that it is possible to consider some interaction between the gradient terms of the components of the system occurring within the nonlocal part of the differential equation or within the nonlocal BCs.…”

“…The approach employed in [14] is the sub-supersolution method. A similar approach has also been used in the recent papers [15,16], while variational methods have been utilized in [17][18][19].…”

Further results of existence of positive solutions of elliptic Kirchhoff equation with general nonlinearity of source terms

“…where we used the subsolution-supersolution method (see previous studies [7][8][9][10][11][12][13][14][15][16][17][18] ), Galerkin approach, and a variational method to prove the existence of positive solutions in different cases depending on the parameters p and . We chose the logarithmic nonlinearity of source terms, because it appears in several branches of physics such as inflationary cosmology, nuclear physics, optics, and geophysics (see previous studies 2,4,12,[19][20][21][22][23] ). With all those specific underlying meaning in physics, the global-in-time well posedness of solution to the problem of evolution equation with such logarithmic-type nonlinearity captures lots of attention.…”

Eigenvalues of elliptic functional differential systems via a Birkhoff--Kellogg type theorem

“…The approach employed in [14] is the sub-supersolution method. The system (1.3) has been studied also by the sub-supersolution method in [8,35,6,7], while variational methods were employed in [19,32,38,49].…”