Analysis of positive solutions for a class of semipositone <i>p</i>-Laplacian problems with nonlinear boundary conditions

Continuum of one‐sign solutions of one‐dimensional Minkowski‐curvature problem with nonlinear boundary conditions

“…Second-order ordinary differential equations with different nonlinear boundary value conditions have much application as well as it is fractional-order generalizations, which have been studied by many authors using different methods, see previous studies [14][15][16][17] (the fixed-point theorems and the fractional Euler method), Drame and Costa 18 (phase plane analysis), Goddard et al 19 and Lee et al 19,20 (time maps technique, the method of sub-supersolutions), other studies, [21][22][23][24] (spline collocations method), Ma and Wang 25 (degree theory and bifurcation techniques), and their references. Motivated above papers, we establish the continuum of positive solutions of the problem (1.1) by the bifurcation theorem under the following assumptions.…”

“…When , the problem () can degenerate to the following nonlinear problem which has been studied by Dunninger and Wang 13 (the method of lower and upper solutions and degree theory). Second‐order ordinary differential equations with different nonlinear boundary value conditions have much application as well as it is fractional‐order generalizations, which have been studied by many authors using different methods, see previous studies 14–17 (the fixed‐point theorems and the fractional Euler method), Drame and Costa 18 (phase plane analysis), Goddard et al 19 and Lee et al 19,20 (time maps technique, the method of sub‐supersolutions), other studies, 21–24 (spline collocations method), Ma and Wang 25 (degree theory and bifurcation techniques), and their references.…”