MULTIPLE POSITIVE SOLUTIONS OF NONLINEAR EIGENVALUE PROBLEMS ASSOCIATED TO A CLASS OF p-LAPLACIAN LIKE OPERATORS
Copyright policy )MULTIPLE POSITIVE SOLUTIONS OF NONLINEAR EIGENVALUE PROBLEMS ASSOCIATED TO A CLASS OF p-LAPLACIAN LIKE OPERATORS
This paper deals with positive solutions of a class of nonlinear eigenvalue problems. For a quasilinear elliptic problem (#) - div (ϕ(|∇u|)∇u) = λf(x,u) in Ω, u = 0 on ∂Ω, we assume asymptotic conditions on ϕ and f such as ϕ(t) ~ tp0-2, f(x,t) ~ tq0-1as t → +0 and ϕ(t) ~ tp1-2, f(x,t) ~ tq1-1as t → ∞. The combined effects of sub-nonlinearity (p0> q0) and super-nonlinearity (p1< q1) with the subcritical term f(x,u) imply the existence of at least two positive solutions of (#) for 0 < λ < Λ.
Bifurcations in context of PDEs, Boundary value problems for second-order elliptic equations, nonlinear eigenvalue problem, minimum solution, Degenerate elliptic equations, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, Nonlinear elliptic equations, multiple positive solution
Bifurcations in context of PDEs, Boundary value problems for second-order elliptic equations, nonlinear eigenvalue problem, minimum solution, Degenerate elliptic equations, Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs, Nonlinear elliptic equations, multiple positive solution
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