No abstract

No abstract

We establish the existence of positive solutions for a nonlinear elliptic Dirichlet problem in dimension N involving the N -Laplacian. The nonlinearity considered depends on the gradient of the unknown function and an exponential term. In such case, variational methods cannot be applied. Our approach is based on approximation scheme, where we consider a new class of normed spaces of finite dimension. As a particular case, we extended the result achieved by De Araujo and Montenegro [2016] for any N > 2.

The existence of at least three weak solutions for a class of differential equations with ( )-Kirchhoff-type and subject to small perturbations of nonhomogeneous Neumann conditions is established under suitable assumptions. Our technical approach is based on variational methods. In addition, an example to illustrate our results is given. K E Y W O R D SVariable exponent Sobolev spaces, ( )-Kirchhoff-type problems, multiple solutions, variational methods M S C ( 2 0 1 0 ) 35J20, 35J60326

No abstract