Abstract We consider a Dirichlet problem driven by the anisotropic ( p z ), q ))-Laplacian, with parametric reaction exhibiting combined effects of singular and concave-convex nonlinearities. The superlinear term may change sign. Using variational tools together truncation comparison techniques, we prove global (for parameter $$\lambda &gt;0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/Ma...

We consider singular problems associated with the weighted anisotropic $p$-Laplace operator $$ H_{p,w}u=\text{div}(w(x)(H(\nabla u))^{p-1}\nabla H(\nabla u)), where $H$ is a Finsler-Minkowski norm and weight $w$ belongs to class of $p$-admissible weights, which may vanish or blow up near origin. discuss existence regularity properties weak solutions for mixed exponential nonlinearities. In part...

The failure of materials and interfaces is mediated by cracks, almost singular dissipative structures that propagate at velocities approaching the speed of sound. Crack initiation and subsequent propagation-the dynamic process of fracture-couples a wide range of time and length scales. Crack dynamics challenge our understanding of the fundamental physics processes that take place in the extreme...