Multiplicity of solutions for parametric p-laplacian equationswith nonlinearity concave near the origin
We consider a nonlinear elliptic problem driven by the p-Laplacian and depending on a parameter. The right-hand side nonlinearity is concave, (i.e., p-sublinear) near the origin. For such problems we prove two multiplicity results, one when the right-hand side nonlinearity is p-linear near infinity and the other when it is p-superlinear. Both results show that there exists an open bounded interval such that the problem has five nontrivial solutions (two positive, two negative and one nodal), if the parameter is in that interval. We also consider the case when the parameter is in the right end of the interval.
Constant sign solutions, Multiple solutions, Nodal solutions, P-Laplacian, P-linear perturbation, P-superlinear perturbation, Upper and lower solutions
Hu, Shouchuan, and Nikolaos S. Papageorgiou. "Multiplicity of solutions for parametric $ p $-Laplacian equations with nonlinearity concave near the origin." Tohoku Mathematical Journal, Second Series 62, no. 1 (2010): 137-162.
Tohoku Mathematical Journal