An elliptic problem with discontinuous sublinear nonlinearities in RN

Multiple positive solutions of singular and critical elliptic problem in $${\mathbb{R}^2}$$ with discontinuous nonlinearities

“…Proof. We adopt the approach as in [14] to the bounded domain set up. The associated functional E λ (u) =…”

“…In [5] authors have discussed the existence and multiplicity for Laplace equation with discontinuous nonlinearities with critical exponents in R n for n ≥ 3. The existence of unique solution with sublinear nonlinearity has been proved in [14]. Existence results for semilinear equation with continuous and exponential nonlinearity motivated from Moser-Trudinger inequality has been extensively studied starting from [1][2][3]10].…”

Elliptic Problems in with Critical and Singular Discontinuous Nonlinearities

“…The problem with jump discontinuity but without the singular term have been studied in [2], [4], [20] and [24]. In all the above mentioned works, the main methods used are variational techniques and the generalized gradient theory for locally Lipschitz functionals as developed in [11] and [12].…”