We consider a Dirichlet problem driven by general nonlinear, nonhomogeneous differential operator. The reaction has the competing effects of singular term and parametric perturbation which is superlinear sign-changing. Using variational tools from critical point theory together with truncation comparison techniques, we show that for all small values parameter, at least two positive smooth solut...

We prove the existence of positive solutions for a class semipositone problems with singular Trudinger-Moser nonlinearities. The proof is based on compactness and regularity arguments.

Mountain pass in a suitable Orlicz space is employed to prove the existence of soliton solutions for a quasilinear Schrödinger equation involving critical exponent in RN . These equations contain strongly singular nonlinearities which include derivatives of the second order. Such equations have been studied as models of several physical phenomena. The nonlinearity here corresponds to the superf...

Reduction operators, i.e., the operators of nonclassical (or conditional) symmetry of a class of variable coefficient nonlinear wave equations with power nonlinearities, are investigated within the framework of a singular reduction operator. A classification of regular reduction operators is performed with respect to generalized extended equivalence groups. Exact solutions of some nonlinear wav...

‎in this paper‎, ‎we study a class of boundary value problem‎ ‎involving the p-laplacian oprator and singular nonlinearities‎. ‎we‎ ‎analyze the existence a critical parameter $lambda^{ast}$ such‎ ‎that the problem has least one solution for‎ ‎$lambdain(0,lambda^{ast})$ and no solution for‎ ‎$lambda>lambda^{ast}.$ we find lower bounds of critical‎ ‎parameter $lambda^{ast}$‎. ‎we use the method ...

In this paper we consider positive solutions of second order quasilinear ordinary differential equations with singular nonlinearities. We obtain the asymptotic equivalence theorems for asymptotically superlinear solutions and decaying solutions. By using these theorems, exact asymptotic forms of such solutions are determined. Furthermore, we can establish the uniqueness of decaying solutions as...

Using minimax methods we study the existence and multiplicity of nontrivial solutions for a singular class of semilinear elliptic nonhomogeneous equation where the potentials can change sign and the nonlinearities may be unbounded in x and behaves like exp(αs2) when |s| → +∞. We establish the existence of two distinct solutions when the perturbation is suitable small.

Abstract A new method for solving the boundary value problems second order ODEs with bounded nonlinearities and singular $$\varphi $$ φ –Laplacians is presented.