Three nontrivial solutions for Neumann problems resonant at any positive eigenvalue

We consider a semilinear Neumann problem with a parametric reaction which has a concave term and a perturbation which at ±∞ can be resonant with respect to any positive eigenvalue. Using variational methods based on the critical point theory and Morse theory, we show that there exists a critical parameter value λ ∗ > 0 such that if λ ∈(0, λ ∗ ), then the problem has at least three nontrivial smooth solutions

A bifurcation-type theorem for the positive solutions of a nonlinear Neumann problem with concave and convex terms

We consider a nonlinear elliptic Neumann problem driven by the p-Laplacian with a reaction that involves the combined effects of a “concave” and of a “convex” terms. The convex term (p-superlinear term) need not satisfy the Ambrosetti-Rabinowitz condition. Employing variational methods based on the critical point theory together with truncation techniques, we prove a bifurcation type theorem for the equation

The spectrum and an index formula for the Neumann P-laplacian and multiple solutions for problems with a crossing nonlinearity

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Convergence in approximation and nonsmooth analysis

Δημοσίευση σε επιστημονικό περιοδικόΜη διαθέσιμη περίληψηNot available summarizationPresented on: Journal of Approximation Theor