We study existence and boundedness of solutions for the quasilinear elliptic equation -Delta(m)u = lambda(1 + u)(p) in a bounded domain Omega with homogeneous Dirichlet boundary conditions. The assumptions on both the parameters lambda and p are fundamental. Strange critical exponents appear when boundedness of solutions is concerned. In our proofs we use techniques from calculus of variations, from critical-point theory, and from the theory of ordinary differential equations
Ferrero, A. (2004). On the solutions of quasilinear elliptic equations with a polynomial-type reaction term. ADVANCES IN DIFFERENTIAL EQUATIONS, 9(11-12), 1201-1234.
On the solutions of quasilinear elliptic equations with a polynomial-type reaction term
Ferrero, A
2004
Abstract
We study existence and boundedness of solutions for the quasilinear elliptic equation -Delta(m)u = lambda(1 + u)(p) in a bounded domain Omega with homogeneous Dirichlet boundary conditions. The assumptions on both the parameters lambda and p are fundamental. Strange critical exponents appear when boundedness of solutions is concerned. In our proofs we use techniques from calculus of variations, from critical-point theory, and from the theory of ordinary differential equations
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