Existence of multiple positive solutions for a semilinear equation with critical exponent

DOI10.1017/S0308210500021028zbMath0789.35059OpenAlexW2023289449MaRDI QIDQ4037717

Yin-Bing Deng

Publication date: 16 May 1993

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0308210500021028

zbMATH Keywords

barrier methodcritical exponentmultiple positive solutionsPokhozhaev identitysemilinear elliptic equation on \(\mathbb{R}^ N\)

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Variational methods for second-order elliptic equations (35J20)

Related Items (10)

Multiplicity and uniqueness of positive solutions for nonhomogeneous semilinear elliptic equation with critical exponent ⋮ Multiple positive solutions for semilinear elliptic equations in ℝ involving critical exponents ⋮ Normalized solutions for critical growth Schrödinger equations with nonautonomous perturbation ⋮ INFINITELY MANY SOLUTIONS FOR A CLASS OF SUBLINEAR SCHRÖDINGER EQUATIONS ⋮ Solutions for a class of singular nonlinear boundary value problem involving critical exponent ⋮ Existence of positive solutions for m-Laplacian equations in N involving critical Sobolev exponents ⋮ Existence and properties of multiple positive solutions for semi-linear equations with critical exponents ⋮ Optimal control problems governed by non-well-posed semilinear elliptic equation ⋮ Entire positive solutions for an inhomogeneous semilinear biharmonic equation ⋮ The existence of nontrivial solutions to nonlinear elliptic equation of \(p\)-\(q\)-Laplacian type on \(\mathbb R^N\)

Cites Work

• A note on the problem \(-\Delta u=\lambda u+u\,| u| ^{2^*-2}\)
• Positive solutions of some nonlinear elliptic problems in exterior domains
• Some existence results for superlinear elliptic boundary value problems involving critical exponents
• On the superlinear Ambrosetti-Prodi problem
• Positive solutions of nonlinear elliptic equations involving critical sobolev exponents
• Bifurcation in L^p (R^N ) for a Semilinear Elliptic Equation
• Existence of multiple positive solutions of inhomogeneous semilinear elliptic problems in unbounded domains
• Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces

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