An exact multiplicity theorem involving concave-convex nonlinearities and its application to stationary solutions of a singular diffusion problem

DOI10.1016/S0362-546X(99)00272-2zbMath0992.34014OpenAlexW2156146125WikidataQ127359287 ScholiaQ127359287MaRDI QIDQ5937338

Shin-Hwa Wang, Dau-Ming Long

Publication date: 19 September 2002

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0362-546x(99)00272-2

zbMATH Keywords

positive solutionsbifurcationtwo-point boundary value problemplasma equationtime map

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Bifurcation theory for ordinary differential equations (34C23) Statistical mechanics of plasmas (82D10) Positive solutions to nonlinear boundary value problems for ordinary differential equations (34B18)

Related Items (12)

Exact multiplicity results for a class of two-point boundary value problems ⋮ Exact number of positive solutions for a class of semipositone problems ⋮ Nondegeneracy and uniqueness of positive solutions for Robin problem of second order ordinary differential equations and its applications ⋮ Ordering properties of positive solutions for a class of \(\varphi\)-Laplacian quasilinear Dirichlet problems ⋮ Exact multiplicity and ordering properties of positive solutions of a \(p\)-Laplacian Dirichlet problem and their applications. ⋮ The positive solutions of boundary value problems for a class of one-dimensional \(p\)-Laplacians ⋮ Exact structure of positive solutions for a \(p\)-Laplacian problem involving singular and superlinear nonlinearities ⋮ Exact structure of positive solutions for some \(p\)-Laplacian equations ⋮ Exact number of solutions for singular Dirichlet boundary value problems ⋮ Global bifurcation and exact multiplicity of positive solutions for a positone problem with cubic nonlinearity and their applications ⋮ Uniqueness results for the one-dimensional \(p\)-Laplacian ⋮ Exact number of positive solutions for semipositone problems

Cites Work

• Global bifurcation of steady-state solutions
• Exact multiplicity results for two classes of boundary value problems
• Quenching, nonquenching, and beyond quenching for solution of some parabolic equations
• Bifurcation, perturbation of simple eigenvalues, and linearized stability
• Stabilization of solutions of a degenerate nonlinear diffusion problem
• Non-negative solutions for a class of non-positone problems
• The critical length for a quenching problem
• Quenching for solutions of a plasma type equation
• On the Existence of Positive Solutions of Semilinear Elliptic Equations
• Exact multiplicity results for boundary value problems with nonlinearities generalising cubic
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