Sturm–Liouville Type Problems for the p-Laplacian under Asymptotic Non-resonance Conditions

Sharp parameter ranges in the uniform anti-maximum principle for second-order ordinary differential operators

“…In this case (3) together with arbitrary homogenous boundary data at r = 0 and r = 1 is a well defined boundary value problem, cf. Reichel, Walter [11]. Our result for (3) is restricted to the case β = 0 .…”

“…We use various first eigenvalues of the Sturm-Liouville problem related to (3). The existence of theses eigenvalues was shown in [11]. …”

Multiplicity Results for Asymptotically Linear Equations, Using the Rotation Number Approach

“…On the other hand, the theory of weighted eigenvalues has been used in order to obtain the existence of at least one solution (not necessarily positive) for semilinear boundary value problems. This approach has been followed, among others, by de Figuereido-Miyagaki in [16] and, more recently, by Reichel-Walter in [43] and by Zhang in [51]. Even if in this setting it is possible to formulate assumptions involving eigenvalues of general order n, the non-triviality of solutions is usually not guaranteed.…”

Inequalities for Eigenfunctions of the P-Laplacian

“…Numerous other authors, see e. g. [2], [3,4], [5], [6], [7] and the bibliographies of these papers, have extended this work in various directions including the study of generalized hyperbolic functions and their inverses. Our goal here to study these p-trigonometric and p-hyperbolic functions and to prove several inequalities for them.…”