Nonhomogeneous Elliptic Equations with Decaying Cylindrical Potential and Critical Exponent

Critical Exponents for Semilinear Equations of Mixed Elliptic-Hyperbolic and Degenerate Types

For semilinear Gellerstedt equations with Tricomi, Goursat, or Dirichlet boundary conditions, we prove Pohožaev-type identities and derive nonexistence results that exploit an invariance of the linear part with respect to certain nonhomogeneous dilations. A critical-exponent phenomenon of power type in the nonlinearity is exhibited in these mixed elliptic-hyperbolic or degenerate settings where...

The Nehari Manifold for a Class of Indefinite Weight Semilinear Elliptic Equations

The Solvability of Concave-Convex Quasilinear Elliptic Systems Involving $p$-Laplacian and Critical Sobolev Exponent

In this work, we study the existence of non-trivial multiple solutions for a class of quasilinear elliptic systems equipped with concave-convex nonlinearities and critical growth terms in bounded domains. By using the variational method, especially Nehari manifold and Palais-Smale condition, we prove the existence and multiplicity results of positive solutions.

Critical Exponent for Semilinear Wave Equations with Space-Dependent Potential

We study the balance between the effect of spatial inhomogeneity of the potential in the dissipative term and the focusing nonlinearity. Sharp critical exponent results will be presented in the case of slow decaying potential.

Bifurcation Analysis of Elliptic Equations Described by Nonhomogeneous Differential Operators

In this article, we are concerned with a class of nonlinear partial differential elliptic equations with Dirichlet boundary data. The key feature of this paper consists in competition effects of two generalized differential operators, which extend the standard operators with variable exponent. This class of problems is motivated by phenomena arising in non-Newtonian fluids or image reconstructi...