On the existence of multiple positive solutions to some superlinear systems

Abstract

We use the method of upper and lower solutions combined with degree-theoretic techniques to prove the existence of multiple positive solutions to some superlinear elliptic systems of the formon a smooth, bounded domain Ω ⊂ R n with Dirichlet boundary conditions, under suitable conditions on g 1 and g 2 . Our techniques apply generally to subcritical, superlinear problems with a certain concave-convex shape to their nonlinearity.

Kirchhoff type equations with strong singularities

“…a contradiction. The strong convergence: u n → u −γ strongly in H 1 0 (Ω) leads then to the estimate (8) of Ω f (x)(u −γ ) −γ ϕdx, thanks to Fatou's Lemma and (6). Case 2.…”

“…(see, e.g. [1][2][3][4][5][6][7][8][9][10][11][12][14][15][16][17][18][19][20][21][22][23][24][25][26][28][29][30][31][32][33][34][36][37][38][39][40][41][42] and references therein). For the singular boundary theory, we refer the reader to the books by Agarwal and O'Regan [1], and Hernández and Mancebo [25] for an excellent introduction to the subject.…”