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In this paper we analyse possible extensions of the classical Steklov eigenvalue problem to the fractional setting. In particular, we find a non-local eigenvalue problem of fractional type that approximates, when taking a suitable limit, the classical Steklov eigenvalue problem.

We consider reaction–diffusion equations under nonlinear boundary conditions where the nonlinearities are asymptotically linear at infinity and depend on a parameter. We prove that, as the parameter crosses some critical values, a resonance-type phenomenon provides solutions that bifurcate from infinity. We characterize the bifurcated branches when they are sub- or supercritical. We obtain both Landesman–Lazer-type conditions that guarantee the existence of solutions in the resonant case and an anti-maximum principle.

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Fractional eigenvalue problems that approximate Steklov eigenvalue problems

Bifurcation from infinity for reaction–diffusion equations under nonlinear boundary conditions

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2 results

Fractional eigenvalue problems that approximate Steklov eigenvalue problems

Bifurcation from infinity for reaction–diffusion equations under nonlinear boundary conditions