Semilinear Neumann problems with indefinite and unbounded potential and crossing nonlinearity

Multiplicity of Solutions for Resonant Neumann Problems with an Indefinite and Unbounded Potential

We examine semilinear Neumann problems driven by the Laplacian plus an unbounded and indefinite potential. The reaction is a Carathéodory function which exhibits linear growth near ±∞. We allow for resonance to occur with respect to a nonprincipal nonnegative eigenvalue, and we prove several multiplicity results. Our approach uses critical point theory, Morse theory and the reduction method (th...

Neumann Problems with Indefinite and Unbounded Potential and Concave Terms

We consider a semilinear parametric Neumann problem driven by the negative Laplacian plus an indefinite and unbounded potential. The reaction is asymptotically linear and exhibits a negative concave term near the origin. Using variational methods together with truncation and perturbation techniques and critical groups, we show that for all small values of the parameter the problem has at least ...

Multiple Solutions for Parametric Neumann Problems with Indefinite and Unbounded Potential

We consider a parametric Neumann problem with an indefinite and unbounded potential. Using a combination of critical point theory with truncation techniques and with Morse theory, we produce four nontrivial smooth weak solutions: one positive, one negative and two nodal (sign changing). AMS Subject Classifications: 35J20, 35J60, 58E05.

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

Computational Solution of Blow-Up Problems for Semilinear Parabolic PDEs on Unbounded Domains

A numerical treatement of a model of semilinear parabolic equations on unbounded domain where the solutions blow up in finite time is presented. The numerical approximation requires selecting an appropriate bounded computational domain. The authors present suitable local absorbing boundary conditions (LABCs) in order to derive the bounded computational domain. A unified approach to derive such ...