Existence and Asymptotic Behavior of Positive Solutions to -Laplacian Equations with Singular Nonlinearities

Existence and regularity of solutions for a class of singular (p(x), q(x))-Laplacian systems

“…where δ, C δ are positive constants independents of λ. Lemma 1. Let u the solution of (2.1) given in [38] for λ large enough. Then, for δ > 0 small enough, it holds…”

“…Proof. By using the fact that w is a subsolution of (2.1), Zhang in [38] showed that w(x) ≤ u(x) for a.e. x ∈ Ω provided λ large enough.…”

“…Moreover, similar arguments explored in the proof of [38,Theorem 4.4] give u 1 , v 1 ∈ C(Ω) and produce constants c 0 , c 1 > 0, with c 0 := c 0 (λ), c 1 := c 1 (λ), such that…”

Existence of solutions for a multi-point boundary value problem with a p ( r ) $p(r)$ -Laplacian

“…Such problems usually arise in the study of image processing, elastic mechanics, electrorheological fluids dynamics, etc. (see [10][11][12][13][14][15][16][17][18]).…”

Existence and asymptotic behavior of positive solutions for variable exponent elliptic systems

“…(see [2,18,29]). Many results have been obtained on this kind of problems, for example [1][2][3][6][7][8][9][10][11][12][13][14][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. In [7], Fan give the regularity of weak solutions for differential equations with variable exponent.…”