Semilinear Elliptic Equations with Generalized Cubic Nonlinearities

Oscillation Theory for Semilinear Elliptic Equations with Arbitrary Nonlinearities

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

A remark on the uniqueness of positive solutions to semilinear elliptic equations with double power nonlinearities

We consider the uniqueness of positive solutions to

Lower order perturbations of critical growth nonlinearities in semilinear elliptic equations

The solvability of semilinear elliptic equations with nonlinearities in the critical growth range depends on the terms with lower order growth. We generalize some known results to a wide class of lower order terms and prove a multiplicity result in the left neighborhood of every eigenvalue of ? when the subcritical term is linear. The proofs are based on variational methods; to assure that the ...

Flatness of Semilinear Parabolic PDEs - A Generalized Cauchy-Kowalevski Approach

A generalized Cauchy-Kowalevski approach is proposed for flatness-based trajectory planning for boundary controlled semilinear systems of PDEs in a one-dimensional spatial domain. For this, the ansatz presented in [16] using formal integration is generalized towards a unified design framework, which covers linear and semilinear PDEs including rather broad classes of nonlinearities arising in ap...